Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0.1%	0%	99.9%	1

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample1.5s (62.9%)

Results

1.5s	8253×	body	128	valid
1.0ms	3×	body	256	valid

preprocess38.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

601×	`fma-def_binary32`
498×	`fma-neg_binary32`
174×	`cancel-sign-sub-inv_binary32`
94×	`sub-neg_binary32`
89×	`unsub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	40	32
2	106	32
3	222	32
4	540	32
5	1153	32
6	1987	32
7	2325	32
8	2405	32
9	2416	32
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(+.f32 (-.f32 1 uy) (*.f32 uy maxCos))
(+.f32 (-.f32 1 maxCos) (*.f32 maxCos ux))
(+.f32 (-.f32 1 ux) (*.f32 ux uy))

Outputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 ux))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (-.f32 1 uy) (*.f32 uy maxCos))
(-.f32 1 (-.f32 uy (*.f32 maxCos uy)))
(fma.f32 maxCos uy (-.f32 1 uy))
(-.f32 (fma.f32 maxCos uy 1) uy)
(+.f32 (-.f32 1 maxCos) (*.f32 maxCos ux))
(+.f32 (-.f32 1 maxCos) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 maxCos))
(-.f32 (fma.f32 ux maxCos 1) maxCos)
(+.f32 (-.f32 1 ux) (*.f32 ux uy))
(fma.f32 ux uy (-.f32 1 ux))
(-.f32 (fma.f32 ux uy 1) ux)

Compiler

Compiled 10 to 7 computations (30% saved)

simplify14.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

199×	`fma-def_binary32`
155×	`fma-neg_binary32`
47×	`cancel-sign-sub-inv_binary32`
34×	`sub-neg_binary32`
26×	`unsub-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	8
2	35	8
3	72	8
4	167	8
5	361	8
6	618	8
7	765	8
8	797	8
9	802	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Outputs
(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
(fma.f32 ux maxCos (-.f32 1 ux))
(-.f32 (fma.f32 ux maxCos 1) ux)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(-.f32 (fma.f32 ux maxCos 1) ux)
	0.1b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Compiler

Compiled 54 to 36 computations (33.3% saved)

localize15.0ms (0.6%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (fma.f32 ux maxCos 1) ux)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	ux	@	-inf	(-.f32 (fma.f32 ux maxCos 1) ux)
1.0ms	ux	@	inf	(-.f32 (fma.f32 ux maxCos 1) ux)
0.0ms	ux	@	0	(-.f32 (fma.f32 ux maxCos 1) ux)
0.0ms	maxCos	@	-inf	(-.f32 (fma.f32 ux maxCos 1) ux)
0.0ms	maxCos	@	inf	(-.f32 (fma.f32 ux maxCos 1) ux)

rewrite36.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

672×	`pow1_binary32`
624×	`add-log-exp_binary32`
624×	`log1p-expm1-u_binary32`
624×	`expm1-log1p-u_binary32`
65×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1632	8

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

Inputs
(-.f32 (fma.f32 ux maxCos 1) ux)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (.f32 (neg.f32 ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 ux) 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 (cbrt.f32 ux)) (pow.f32 (cbrt.f32 ux) 2) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 (sqrt.f32 ux)) (sqrt.f32 ux) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 ux maxCos) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 ux maxCos) (+.f32 1 (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (neg.f32 ux) (fma.f32 ux maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (-.f32 (fma.f32 ux maxCos 1) ux))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 (fma.f32 ux maxCos 1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) (pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2) (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3)) (/.f32 1 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux (+.f32 ux (fma.f32 ux maxCos 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux ux)) (/.f32 1 (+.f32 ux (fma.f32 ux maxCos 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)) (-.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux (+.f32 ux (fma.f32 ux maxCos 1)))) (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 ux (fma.f32 ux maxCos 1)) (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux (+.f32 ux (fma.f32 ux maxCos 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux ux)) (+.f32 ux (fma.f32 ux maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3))) (neg.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux (+.f32 ux (fma.f32 ux maxCos 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 ux ux))) (neg.f32 (+.f32 ux (fma.f32 ux maxCos 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 (neg.f32 ux) 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (-.f32 (.f32 (neg.f32 ux) (neg.f32 ux)) (.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (.f32 (neg.f32 ux) (neg.f32 ux))) (-.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (-.f32 (fma.f32 ux maxCos 1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos 1)) 2) (cbrt.f32 (fma.f32 ux maxCos 1)) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 (fma.f32 ux maxCos 1)) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 ux maxCos 1) (*.f32 (neg.f32 ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 ux) 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 (cbrt.f32 ux)) (pow.f32 (cbrt.f32 ux) 2) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (fma.f32 (neg.f32 (sqrt.f32 ux)) (sqrt.f32 ux) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux maxCos) (-.f32 1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux maxCos) (+.f32 1 (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (neg.f32 ux) (fma.f32 ux maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (-.f32 (fma.f32 ux maxCos 1) ux))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) (pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2) (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3)) (/.f32 1 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux (+.f32 ux (fma.f32 ux maxCos 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux ux)) (/.f32 1 (+.f32 ux (fma.f32 ux maxCos 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)) (-.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux (+.f32 ux (fma.f32 ux maxCos 1)))) (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 ux (fma.f32 ux maxCos 1)) (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux (+.f32 ux (fma.f32 ux maxCos 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux ux)) (+.f32 ux (fma.f32 ux maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 ux 3))) (neg.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux (+.f32 ux (fma.f32 ux maxCos 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 ux ux))) (neg.f32 (+.f32 ux (fma.f32 ux maxCos 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 (neg.f32 ux) 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (-.f32 (*.f32 (neg.f32 ux) (neg.f32 ux)) (*.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (*.f32 (neg.f32 ux) (neg.f32 ux))) (-.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (-.f32 (fma.f32 ux maxCos 1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (-.f32 (fma.f32 ux maxCos 1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (-.f32 (fma.f32 ux maxCos 1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (fma.f32 ux maxCos 1) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (fma.f32 ux maxCos 1)) 2) (cbrt.f32 (fma.f32 ux maxCos 1)) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 (fma.f32 ux maxCos 1)) (neg.f32 ux))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))))))

simplify19.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

185×	`fma-def_binary32`
158×	`fma-neg_binary32`
31×	`sub-neg_binary32`
25×	`unsub-neg_binary32`
22×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	207
1	45	171
2	107	171
3	227	171
4	461	171
5	662	171
6	762	171
7	780	171

Stop Event

1×

saturated

Counts

62 → 48

Calls

Call 1

Inputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(-.f32 1 ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)

Outputs
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos))))
(*.f32 (+.f32 maxCos -1) ux)
(-.f32 (*.f32 maxCos ux) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(+.f32 1 (.f32 -1 (.f32 ux (+.f32 1 (*.f32 -1 maxCos)))))
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 1 ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(*.f32 maxCos ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)
(-.f32 (+.f32 1 (*.f32 maxCos ux)) ux)
(+.f32 1 (*.f32 (+.f32 maxCos -1) ux))
(-.f32 (fma.f32 maxCos ux 1) ux)

prune45.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Error

Counts

50 → 4

Alt Table

Status	Error	Program
	0.5b	(expm1.f32 (log1p.f32 (-.f32 (fma.f32 ux maxCos 1) ux)))
	0.4b	(/.f32 (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 3) (pow.f32 (neg.f32 ux) 3)) (+.f32 (pow.f32 (fma.f32 ux maxCos 1) 2) (-.f32 (.f32 (neg.f32 ux) (neg.f32 ux)) (.f32 (fma.f32 ux maxCos 1) (neg.f32 ux)))))
	0.5b	(*.f32 (+.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)) (-.f32 (sqrt.f32 (fma.f32 ux maxCos 1)) (sqrt.f32 ux)))
▶	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))

Compiler

Compiled 742 to 458 computations (38.3% saved)

localize17.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
✓	0.1b	(*.f32 (-.f32 maxCos 1) ux)

series5.0ms (0.2%)

Counts

2 → 27

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	ux	@	inf	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
1.0ms	maxCos	@	0	(*.f32 (-.f32 maxCos 1) ux)
1.0ms	ux	@	inf	(*.f32 (-.f32 maxCos 1) ux)
0.0ms	ux	@	-inf	(*.f32 (-.f32 maxCos 1) ux)
0.0ms	ux	@	0	(*.f32 (-.f32 maxCos 1) ux)

rewrite38.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`pow1_binary32`
742×	`log1p-expm1-u_binary32`
742×	`expm1-log1p-u_binary32`
79×	`add-sqr-sqrt_binary32`
76×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	152	15
2	2042	15

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

Inputs
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 maxCos ux) (.f32 -1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 ux maxCos) (.f32 ux -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (+.f32 (pow.f32 maxCos 3) -1) ux) (fma.f32 maxCos maxCos (+.f32 maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (fma.f32 maxCos maxCos -1) ux) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 ux (+.f32 (pow.f32 maxCos 3) -1)) (fma.f32 maxCos maxCos (+.f32 maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 ux (fma.f32 maxCos maxCos -1)) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (+.f32 maxCos -1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (+.f32 maxCos -1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 ux) (+.f32 maxCos -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (+.f32 maxCos -1) ux)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 (+.f32 maxCos -1) ux 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 1 (-.f32 1 (.f32 (+.f32 maxCos -1) ux))) (/.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2) (-.f32 1 (.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (fma.f32 (+.f32 maxCos -1) ux 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) (pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2) (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 3)) (/.f32 1 (+.f32 1 (-.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2) (.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2)) (/.f32 1 (-.f32 1 (.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 1 (-.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2) (.f32 (+.f32 maxCos -1) ux))) (+.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 1 (.f32 (+.f32 maxCos -1) ux)) (-.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 1 (-.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2) (.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2) (-.f32 1 (.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2)) (-.f32 1 (.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 3))) (neg.f32 (+.f32 1 (-.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2) (.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 1 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2))) (neg.f32 (-.f32 1 (.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (.f32 (+.f32 maxCos -1) ux) 2) 1) (-.f32 (.f32 (+.f32 maxCos -1) ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 (+.f32 maxCos -1) ux 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (+.f32 maxCos -1) ux 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 ux (+.f32 maxCos -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (.f32 (+.f32 maxCos -1) ux)) 2) (cbrt.f32 (.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (.f32 (+.f32 maxCos -1) ux)) (sqrt.f32 (.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log1p.f32 (.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)) 1))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 maxCos ux) (*.f32 -1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux maxCos) (*.f32 ux -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (pow.f32 maxCos 3) -1) ux) (fma.f32 maxCos maxCos (+.f32 maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (fma.f32 maxCos maxCos -1) ux) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 ux (+.f32 (pow.f32 maxCos 3) -1)) (fma.f32 maxCos maxCos (+.f32 maxCos 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 ux (fma.f32 maxCos maxCos -1)) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 ux) (+.f32 maxCos -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (+.f32 maxCos -1) ux)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 (+.f32 maxCos -1) ux 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 1 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))) (/.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (fma.f32 (+.f32 maxCos -1) ux 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) (pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2) (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (/.f32 1 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2)) (/.f32 1 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux))) (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux)) (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2)) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))) (neg.f32 (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))) (neg.f32 (-.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) 1) (-.f32 (*.f32 (+.f32 maxCos -1) ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 (+.f32 maxCos -1) ux 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 (+.f32 maxCos -1) ux 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 (+.f32 maxCos -1) ux 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (+.f32 maxCos -1) ux 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 ux (+.f32 maxCos -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 2) (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 (+.f32 maxCos -1) ux 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)) 1))))))

simplify24.0ms (1%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary32`
186×	`fma-neg_binary32`
59×	`cancel-sign-sub-inv_binary32`
32×	`sub-neg_binary32`
31×	`associate--r+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	201
1	31	173
2	46	173
3	64	173
4	96	173
5	155	173
6	311	173
7	522	173
8	733	173
9	822	173
10	846	173
11	847	173

Stop Event

1×

saturated

Counts

80 → 65

Calls

Call 1

Inputs
(*.f32 -1 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
1
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)

Outputs
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(fma.f32 ux maxCos (-.f32 1 ux))
1
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)

prune59.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	65	4	69

Error

Counts

69 → 4

Alt Table

Status	Error	Program
▶	0.0b	(exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
	0.5b	(+.f32 1 (log.f32 (pow.f32 (exp.f32 ux) (+.f32 maxCos -1))))
	0.1b	(+.f32 1 (pow.f32 (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 3))
✓	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))

Compiler

Compiled 825 to 622 computations (24.6% saved)

localize19.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
✓	0.0b	(log1p.f32 (*.f32 (+.f32 maxCos -1) ux))
✓	0.1b	(*.f32 (+.f32 maxCos -1) ux)

series39.0ms (1.6%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
15.0ms	ux	@	inf	(exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
12.0ms	ux	@	-inf	(exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
2.0ms	maxCos	@	-inf	(exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
1.0ms	maxCos	@	inf	(exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
1.0ms	maxCos	@	0	(log1p.f32 (*.f32 (+.f32 maxCos -1) ux))

rewrite41.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`pow1_binary32`
724×	`expm1-log1p-u_binary32`
723×	`log1p-expm1-u_binary32`
80×	`add-sqr-sqrt_binary32`
78×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	158	26
2	1928	26

Stop Event

1×	node limit

Counts

3 → 65

Calls

Call 1

Inputs
(*.f32 (+.f32 maxCos -1) ux)
(log1p.f32 (*.f32 (+.f32 maxCos -1) ux))
(exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 maxCos ux) (*.f32 -1 ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 -1 ux) (*.f32 maxCos ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux maxCos) (*.f32 ux -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 ux -1) (*.f32 ux maxCos))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 -1 (pow.f32 maxCos 3)) ux) (fma.f32 maxCos maxCos (-.f32 1 (*.f32 maxCos -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (fma.f32 maxCos maxCos -1) ux) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 ux (+.f32 -1 (pow.f32 maxCos 3))) (fma.f32 maxCos maxCos (-.f32 1 (*.f32 maxCos -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 ux (fma.f32 maxCos maxCos -1)) (+.f32 maxCos 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (+.f32 maxCos -1) ux)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 ux) (+.f32 maxCos -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (+.f32 maxCos -1) 3) (pow.f32 ux 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 ux 3) (pow.f32 (+.f32 maxCos -1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (+.f32 maxCos -1) ux)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1))) (log.f32 (sqrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)) 2)) (log.f32 (cbrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) 2) (cbrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) (sqrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 1 (*.f32 (+.f32 maxCos -1) ux))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)) (pow.f32 (cbrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)) 2) (cbrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)) (sqrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2)) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))) (sqrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) 2)) (cbrt.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (+.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))))))

simplify48.0ms (2%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-in_binary32`
544×	`distribute-lft-in_binary32`
188×	`fma-def_binary32`
156×	`+-commutative_binary32`
141×	`associate-+r+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	1799
1	694	1588
2	2781	1350

Stop Event

1×	node limit

Counts

137 → 146

Calls

Call 1

Inputs
(*.f32 -1 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 maxCos ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 (-.f32 maxCos 1) ux)
(log.f32 (+.f32 (*.f32 -1 ux) 1))
(+.f32 (log.f32 (+.f32 (.f32 -1 ux) 1)) (/.f32 (.f32 maxCos ux) (+.f32 (*.f32 -1 ux) 1)))
(+.f32 (log.f32 (+.f32 (.f32 -1 ux) 1)) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (/.f32 (.f32 maxCos ux) (+.f32 (.f32 -1 ux) 1))))
(+.f32 (log.f32 (+.f32 (.f32 -1 ux) 1)) (+.f32 (.f32 1/3 (/.f32 (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (/.f32 (.f32 maxCos ux) (+.f32 (*.f32 -1 ux) 1)))))
(+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (+.f32 (/.f32 1 (.f32 maxCos ux)) (log.f32 ux))) (/.f32 1 maxCos))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (+.f32 (/.f32 1 (.f32 maxCos ux)) (+.f32 (log.f32 ux) (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))))) (/.f32 1 maxCos))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (+.f32 (/.f32 1 (.f32 maxCos ux)) (+.f32 (.f32 1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)))) (+.f32 (log.f32 ux) (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)))))))) (/.f32 1 maxCos))
(+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))
(+.f32 (/.f32 1 (.f32 maxCos ux)) (+.f32 (/.f32 -1 maxCos) (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (*.f32 -1 ux)))))
(-.f32 (+.f32 (/.f32 1 (.f32 maxCos ux)) (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)))) (log.f32 (.f32 -1 ux))))) (/.f32 1 maxCos))
(-.f32 (+.f32 (/.f32 1 (.f32 maxCos ux)) (+.f32 (.f32 1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)))) (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)))) (log.f32 (*.f32 -1 ux)))))) (/.f32 1 maxCos))
(*.f32 (-.f32 maxCos 1) ux)
(+.f32 (.f32 -1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (.f32 -1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (.f32 -1/4 (.f32 (pow.f32 (-.f32 maxCos 1) 4) (pow.f32 ux 4))) (+.f32 (.f32 -1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3))) (*.f32 (-.f32 maxCos 1) ux))))
(+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))
(+.f32 (log.f32 (-.f32 maxCos 1)) (+.f32 (.f32 -1 (log.f32 (/.f32 1 ux))) (/.f32 1 (.f32 (-.f32 maxCos 1) ux))))
(-.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (+.f32 (.f32 -1 (log.f32 (/.f32 1 ux))) (/.f32 1 (.f32 (-.f32 maxCos 1) ux)))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2)))))
(-.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (+.f32 (.f32 -1 (log.f32 (/.f32 1 ux))) (+.f32 (.f32 1/3 (/.f32 1 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3)))) (/.f32 1 (.f32 (-.f32 maxCos 1) ux))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2)))))
(+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))
(+.f32 (log.f32 (.f32 -1 (-.f32 maxCos 1))) (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (/.f32 1 (*.f32 (-.f32 maxCos 1) ux))))
(-.f32 (+.f32 (log.f32 (.f32 -1 (-.f32 maxCos 1))) (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (/.f32 1 (.f32 (-.f32 maxCos 1) ux)))) (.f32 1/2 (/.f32 1 (*.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2)))))
(-.f32 (+.f32 (log.f32 (.f32 -1 (-.f32 maxCos 1))) (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (+.f32 (.f32 1/3 (/.f32 1 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3)))) (/.f32 1 (.f32 (-.f32 maxCos 1) ux))))) (.f32 1/2 (/.f32 1 (*.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2)))))
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (+.f32 (.f32 maxCos ux) (.f32 (+.f32 (.f32 1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (.f32 -1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)))) (.f32 (pow.f32 maxCos 2) (+.f32 (*.f32 -1 ux) 1))))))
(+.f32 (.f32 (pow.f32 maxCos 3) (.f32 (+.f32 (.f32 1/3 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (+.f32 (.f32 1/6 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (.f32 -1/2 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))))) (+.f32 (.f32 -1 ux) 1))) (+.f32 (.f32 -1 ux) (+.f32 1 (+.f32 (.f32 maxCos ux) (.f32 (+.f32 (.f32 1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (.f32 -1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)))) (.f32 (pow.f32 maxCos 2) (+.f32 (.f32 -1 ux) 1)))))))
(exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (pow.f32 (-.f32 (/.f32 1 ux) 1) 2))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) (pow.f32 maxCos 2))))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)) (pow.f32 ux 2))) (+.f32 (.f32 1/6 (pow.f32 (-.f32 (/.f32 1 ux) 1) 3)) (.f32 1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) (pow.f32 maxCos 3)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos) (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (pow.f32 (-.f32 (/.f32 1 ux) 1) 2)))) (pow.f32 maxCos 2)))))
(exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))
(+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (*.f32 -1 ux)))))
(+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))))) (pow.f32 maxCos 2)) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 (.f32 -1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))) (.f32 -1/6 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))) (pow.f32 maxCos 3))) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))) (pow.f32 maxCos 2)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))))))
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (+.f32 (.f32 (-.f32 maxCos 1) ux) (.f32 (+.f32 (.f32 1/2 (pow.f32 (-.f32 maxCos 1) 2)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 2))) (pow.f32 ux 2))))
(+.f32 1 (+.f32 (.f32 (+.f32 (.f32 1/6 (pow.f32 (-.f32 maxCos 1) 3)) (+.f32 (.f32 1/3 (pow.f32 (-.f32 maxCos 1) 3)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 3)))) (pow.f32 ux 3)) (+.f32 (.f32 (-.f32 maxCos 1) ux) (.f32 (+.f32 (.f32 1/2 (pow.f32 (-.f32 maxCos 1) 2)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 2))) (pow.f32 ux 2)))))
(exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux)))))
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1)))))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))

Outputs
(*.f32 -1 ux)
(neg.f32 ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1 ux) (.f32 maxCos ux))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(log.f32 (+.f32 (*.f32 -1 ux) 1))
(log.f32 (fma.f32 -1 ux 1))
(log1p.f32 (neg.f32 ux))
(+.f32 (log.f32 (+.f32 (.f32 -1 ux) 1)) (/.f32 (.f32 maxCos ux) (+.f32 (*.f32 -1 ux) 1)))
(+.f32 (log.f32 (fma.f32 -1 ux 1)) (/.f32 (*.f32 ux maxCos) (fma.f32 -1 ux 1)))
(+.f32 (log1p.f32 (neg.f32 ux)) (*.f32 (/.f32 maxCos (-.f32 1 ux)) ux))
(+.f32 (log1p.f32 (neg.f32 ux)) (/.f32 maxCos (+.f32 -1 (/.f32 1 ux))))
(+.f32 (log.f32 (+.f32 (.f32 -1 ux) 1)) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (/.f32 (.f32 maxCos ux) (+.f32 (.f32 -1 ux) 1))))
(+.f32 (log.f32 (fma.f32 -1 ux 1)) (fma.f32 -1/2 (/.f32 (.f32 (.f32 maxCos maxCos) (.f32 ux ux)) (pow.f32 (fma.f32 -1 ux 1) 2)) (/.f32 (.f32 ux maxCos) (fma.f32 -1 ux 1))))
(+.f32 (log1p.f32 (neg.f32 ux)) (fma.f32 -1/2 (.f32 (/.f32 (.f32 maxCos maxCos) (pow.f32 (-.f32 1 ux) 2)) (.f32 ux ux)) (.f32 (/.f32 maxCos (-.f32 1 ux)) ux)))
(+.f32 (log1p.f32 (neg.f32 ux)) (fma.f32 -1/2 (/.f32 maxCos (/.f32 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 2) maxCos)) (/.f32 maxCos (+.f32 -1 (/.f32 1 ux)))))
(+.f32 (log.f32 (+.f32 (.f32 -1 ux) 1)) (+.f32 (.f32 1/3 (/.f32 (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (/.f32 (.f32 maxCos ux) (+.f32 (*.f32 -1 ux) 1)))))
(+.f32 (log.f32 (fma.f32 -1 ux 1)) (fma.f32 1/3 (/.f32 (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)) (pow.f32 (fma.f32 -1 ux 1) 3)) (fma.f32 -1/2 (/.f32 (.f32 (.f32 maxCos maxCos) (.f32 ux ux)) (pow.f32 (fma.f32 -1 ux 1) 2)) (/.f32 (*.f32 ux maxCos) (fma.f32 -1 ux 1)))))
(+.f32 (log1p.f32 (neg.f32 ux)) (fma.f32 1/3 (/.f32 (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)) (pow.f32 (-.f32 1 ux) 3)) (fma.f32 -1/2 (.f32 (/.f32 (.f32 maxCos maxCos) (pow.f32 (-.f32 1 ux) 2)) (.f32 ux ux)) (*.f32 (/.f32 maxCos (-.f32 1 ux)) ux))))
(+.f32 (log1p.f32 (neg.f32 ux)) (fma.f32 1/3 (/.f32 (pow.f32 maxCos 3) (pow.f32 (+.f32 -1 (/.f32 1 ux)) 3)) (fma.f32 -1/2 (/.f32 maxCos (/.f32 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 2) maxCos)) (/.f32 maxCos (+.f32 -1 (/.f32 1 ux))))))
(+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))
(fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))
(+.f32 (log.f32 maxCos) (log.f32 ux))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (+.f32 (/.f32 1 (.f32 maxCos ux)) (log.f32 ux))) (/.f32 1 maxCos))
(-.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (+.f32 (log.f32 ux) (/.f32 (/.f32 1 maxCos) ux))) (/.f32 1 maxCos))
(+.f32 (log.f32 maxCos) (+.f32 (/.f32 (/.f32 1 maxCos) ux) (-.f32 (log.f32 ux) (/.f32 1 maxCos))))
(+.f32 (log.f32 maxCos) (+.f32 (log.f32 ux) (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos)))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (+.f32 (/.f32 1 (.f32 maxCos ux)) (+.f32 (log.f32 ux) (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (*.f32 (pow.f32 maxCos 2) (pow.f32 ux 2))))))) (/.f32 1 maxCos))
(-.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (+.f32 (/.f32 (/.f32 1 maxCos) ux) (+.f32 (log.f32 ux) (.f32 -1/2 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 2) (.f32 (.f32 maxCos maxCos) (.f32 ux ux))))))) (/.f32 1 maxCos))
(+.f32 (log.f32 maxCos) (+.f32 (fma.f32 -1/2 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 maxCos (.f32 maxCos (*.f32 ux ux)))) (log.f32 ux)) (-.f32 (/.f32 (/.f32 1 maxCos) ux) (/.f32 1 maxCos))))
(+.f32 (log.f32 maxCos) (+.f32 (fma.f32 -1/2 (/.f32 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 2) (*.f32 maxCos maxCos)) (log.f32 ux)) (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos)))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (+.f32 (/.f32 1 (.f32 maxCos ux)) (+.f32 (.f32 1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3)))) (+.f32 (log.f32 ux) (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (.f32 (pow.f32 maxCos 2) (pow.f32 ux 2)))))))) (/.f32 1 maxCos))
(-.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (+.f32 (/.f32 (/.f32 1 maxCos) ux) (fma.f32 1/3 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 3) (.f32 (pow.f32 maxCos 3) (pow.f32 ux 3))) (+.f32 (log.f32 ux) (.f32 -1/2 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 2) (.f32 (.f32 maxCos maxCos) (*.f32 ux ux)))))))) (/.f32 1 maxCos))
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(*.f32 (-.f32 maxCos 1) ux)
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (.f32 -1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (*.f32 (-.f32 maxCos 1) ux))
(fma.f32 -1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 maxCos -1) 2)) (*.f32 ux (+.f32 maxCos -1)))
(fma.f32 ux (+.f32 -1 maxCos) (.f32 -1/2 (.f32 ux (*.f32 ux (pow.f32 (+.f32 -1 maxCos) 2)))))
(.f32 ux (+.f32 (+.f32 -1 maxCos) (.f32 (*.f32 -1/2 (pow.f32 (+.f32 -1 maxCos) 2)) ux)))
(+.f32 (.f32 -1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3))) (*.f32 (-.f32 maxCos 1) ux)))
(fma.f32 -1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 maxCos -1) 2)) (fma.f32 1/3 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 maxCos -1) 3)) (.f32 ux (+.f32 maxCos -1))))
(fma.f32 -1/2 (.f32 ux (.f32 ux (pow.f32 (+.f32 -1 maxCos) 2))) (fma.f32 ux (+.f32 -1 maxCos) (.f32 1/3 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 -1 maxCos) 3)))))
(fma.f32 -1/2 (.f32 ux (.f32 ux (pow.f32 (+.f32 -1 maxCos) 2))) (fma.f32 ux (+.f32 -1 maxCos) (.f32 (pow.f32 (+.f32 -1 maxCos) 3) (.f32 1/3 (pow.f32 ux 3)))))
(+.f32 (.f32 -1/4 (.f32 (pow.f32 (-.f32 maxCos 1) 4) (pow.f32 ux 4))) (+.f32 (.f32 -1/2 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3))) (*.f32 (-.f32 maxCos 1) ux))))
(fma.f32 -1/4 (.f32 (pow.f32 (+.f32 maxCos -1) 4) (pow.f32 ux 4)) (fma.f32 -1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 maxCos -1) 2)) (fma.f32 1/3 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 maxCos -1) 3)) (*.f32 ux (+.f32 maxCos -1)))))
(fma.f32 -1/4 (.f32 (pow.f32 (+.f32 -1 maxCos) 4) (pow.f32 ux 4)) (fma.f32 -1/2 (.f32 ux (.f32 ux (pow.f32 (+.f32 -1 maxCos) 2))) (fma.f32 ux (+.f32 -1 maxCos) (.f32 1/3 (*.f32 (pow.f32 ux 3) (pow.f32 (+.f32 -1 maxCos) 3))))))
(fma.f32 -1/4 (.f32 (pow.f32 (+.f32 -1 maxCos) 4) (pow.f32 ux 4)) (fma.f32 -1/2 (.f32 ux (.f32 ux (pow.f32 (+.f32 -1 maxCos) 2))) (fma.f32 ux (+.f32 -1 maxCos) (.f32 (pow.f32 (+.f32 -1 maxCos) 3) (*.f32 1/3 (pow.f32 ux 3))))))
(+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))
(+.f32 (log.f32 (+.f32 maxCos -1)) (neg.f32 (neg.f32 (log.f32 ux))))
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(+.f32 (log.f32 ux) (+.f32 (/.f32 1 (-.f32 (*.f32 ux maxCos) ux)) (log.f32 (+.f32 -1 maxCos))))
(-.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (+.f32 (.f32 -1 (log.f32 (/.f32 1 ux))) (/.f32 1 (.f32 (-.f32 maxCos 1) ux)))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2)))))
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(+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))
(fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))
(-.f32 (log.f32 (+.f32 (neg.f32 maxCos) 1)) (log.f32 (/.f32 -1 ux)))
(-.f32 (log.f32 (+.f32 1 (neg.f32 maxCos))) (log.f32 (/.f32 -1 ux)))
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(+.f32 (/.f32 1 (*.f32 ux (+.f32 -1 maxCos))) (-.f32 (log.f32 (+.f32 (neg.f32 maxCos) 1)) (log.f32 (/.f32 -1 ux))))
(+.f32 (/.f32 1 (-.f32 (*.f32 ux maxCos) ux)) (-.f32 (log.f32 (+.f32 1 (neg.f32 maxCos))) (log.f32 (/.f32 -1 ux))))
(-.f32 (+.f32 (log.f32 (.f32 -1 (-.f32 maxCos 1))) (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (/.f32 1 (.f32 (-.f32 maxCos 1) ux)))) (.f32 1/2 (/.f32 1 (*.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2)))))
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(-.f32 (+.f32 (log.f32 (.f32 -1 (-.f32 maxCos 1))) (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (+.f32 (.f32 1/3 (/.f32 1 (.f32 (pow.f32 (-.f32 maxCos 1) 3) (pow.f32 ux 3)))) (/.f32 1 (.f32 (-.f32 maxCos 1) ux))))) (.f32 1/2 (/.f32 1 (*.f32 (pow.f32 (-.f32 maxCos 1) 2) (pow.f32 ux 2)))))
(-.f32 (+.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1)))) (+.f32 (/.f32 1 (.f32 ux (+.f32 maxCos -1))) (/.f32 1/3 (.f32 (pow.f32 ux 3) (pow.f32 (+.f32 maxCos -1) 3))))) (/.f32 1/2 (.f32 (.f32 ux ux) (pow.f32 (+.f32 maxCos -1) 2))))
(+.f32 (log.f32 (+.f32 (neg.f32 maxCos) 1)) (+.f32 (-.f32 (+.f32 (/.f32 1 (.f32 ux (+.f32 -1 maxCos))) (/.f32 (/.f32 1/3 (pow.f32 ux 3)) (pow.f32 (+.f32 -1 maxCos) 3))) (log.f32 (/.f32 -1 ux))) (/.f32 -1/2 (.f32 ux (*.f32 ux (pow.f32 (+.f32 -1 maxCos) 2))))))
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(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
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(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (.f32 (pow.f32 maxCos 3) (.f32 (+.f32 (.f32 1/3 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (+.f32 (.f32 1/6 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (.f32 -1/2 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))))) (+.f32 (.f32 -1 ux) 1))) (+.f32 (.f32 -1 ux) (+.f32 1 (+.f32 (.f32 maxCos ux) (.f32 (+.f32 (.f32 1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (.f32 -1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)))) (.f32 (pow.f32 maxCos 2) (+.f32 (.f32 -1 ux) 1)))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))
(*.f32 ux maxCos)
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos))
(+.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))) (/.f32 (+.f32 (/.f32 1 ux) -1) (/.f32 maxCos (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))))
(fma.f32 (exp.f32 (log.f32 maxCos)) ux (/.f32 (*.f32 ux (exp.f32 (log.f32 maxCos))) (/.f32 maxCos (+.f32 -1 (/.f32 1 ux)))))
(.f32 (+.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) 1) (.f32 ux maxCos))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (pow.f32 (-.f32 (/.f32 1 ux) 1) 2))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) (pow.f32 maxCos 2))))
(+.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))) (+.f32 (/.f32 (+.f32 (/.f32 1 ux) -1) (/.f32 maxCos (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))) (/.f32 (fma.f32 -1/2 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 2) (.f32 ux ux)) (.f32 1/2 (pow.f32 (+.f32 (/.f32 1 ux) -1) 2))) (/.f32 (*.f32 maxCos maxCos) (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux)))))))
(+.f32 (fma.f32 (exp.f32 (log.f32 maxCos)) ux (/.f32 (.f32 ux (exp.f32 (log.f32 maxCos))) (/.f32 maxCos (+.f32 -1 (/.f32 1 ux))))) (.f32 (/.f32 (.f32 ux (exp.f32 (log.f32 maxCos))) maxCos) (/.f32 (fma.f32 -1/2 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux ux)) (*.f32 1/2 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 2))) maxCos)))
(+.f32 (.f32 (+.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) 1) (.f32 ux maxCos)) 0)
(+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)) (pow.f32 ux 2))) (+.f32 (.f32 1/6 (pow.f32 (-.f32 (/.f32 1 ux) 1) 3)) (.f32 1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) (pow.f32 maxCos 3)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos) (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (pow.f32 (-.f32 (/.f32 1 ux) 1) 2)))) (pow.f32 maxCos 2)))))
(+.f32 (/.f32 (fma.f32 -1/2 (/.f32 (+.f32 (/.f32 1 ux) -1) (/.f32 (.f32 ux ux) (pow.f32 (fma.f32 -1 ux 1) 2))) (fma.f32 1/6 (pow.f32 (+.f32 (/.f32 1 ux) -1) 3) (.f32 1/3 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 3) (pow.f32 ux 3))))) (/.f32 (pow.f32 maxCos 3) (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))) (+.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))) (+.f32 (/.f32 (+.f32 (/.f32 1 ux) -1) (/.f32 maxCos (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))) (/.f32 (fma.f32 -1/2 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 2) (.f32 ux ux)) (.f32 1/2 (pow.f32 (+.f32 (/.f32 1 ux) -1) 2))) (/.f32 (*.f32 maxCos maxCos) (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))))))
(+.f32 (fma.f32 (exp.f32 (log.f32 maxCos)) ux (/.f32 (.f32 ux (exp.f32 (log.f32 maxCos))) (/.f32 maxCos (+.f32 -1 (/.f32 1 ux))))) (+.f32 (.f32 (/.f32 (.f32 ux (exp.f32 (log.f32 maxCos))) maxCos) (/.f32 (fma.f32 -1/2 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux ux)) (.f32 1/2 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 2))) maxCos)) (.f32 (/.f32 (fma.f32 -1/2 (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (/.f32 (+.f32 -1 (/.f32 1 ux)) ux)) (fma.f32 1/3 (/.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 ux 3)) (.f32 1/6 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 3)))) (pow.f32 maxCos 3)) (*.f32 ux (exp.f32 (log.f32 maxCos))))))
(+.f32 (.f32 (+.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) 1) (.f32 ux maxCos)) (+.f32 0 (/.f32 (fma.f32 -1/2 (.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) (.f32 ux ux)) (pow.f32 (-.f32 1 ux) 2)) (+.f32 (.f32 1/2 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 3)) 0)) (/.f32 (pow.f32 maxCos 3) (.f32 ux maxCos)))))
(exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))
(exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux))))
(*.f32 (neg.f32 ux) (pow.f32 (/.f32 -1 maxCos) -1))
(/.f32 (neg.f32 ux) (/.f32 -1 maxCos))
(+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (*.f32 -1 ux)))))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (/.f32 (*.f32 ux maxCos) (fma.f32 -1 ux 1))))
(fma.f32 (pow.f32 (/.f32 -1 maxCos) -1) (neg.f32 ux) (/.f32 (.f32 (pow.f32 (/.f32 -1 maxCos) -1) (.f32 (neg.f32 ux) (-.f32 1 ux))) (*.f32 ux maxCos)))
(fma.f32 (/.f32 (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)) maxCos) (+.f32 -1 (/.f32 1 ux)) (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)))
(+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))))) (pow.f32 maxCos 2)) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (/.f32 (*.f32 ux maxCos) (fma.f32 -1 ux 1))))
(fma.f32 (pow.f32 (/.f32 -1 maxCos) -1) (neg.f32 ux) (/.f32 (.f32 (pow.f32 (/.f32 -1 maxCos) -1) (.f32 (neg.f32 ux) (-.f32 1 ux))) (*.f32 ux maxCos)))
(fma.f32 (/.f32 (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)) maxCos) (+.f32 -1 (/.f32 1 ux)) (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 (.f32 -1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))) (.f32 -1/6 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))) (pow.f32 maxCos 3))) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))) (pow.f32 maxCos 2)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))))))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (/.f32 (*.f32 ux maxCos) (fma.f32 -1 ux 1))))
(fma.f32 (pow.f32 (/.f32 -1 maxCos) -1) (neg.f32 ux) (/.f32 (.f32 (pow.f32 (/.f32 -1 maxCos) -1) (.f32 (neg.f32 ux) (-.f32 1 ux))) (*.f32 ux maxCos)))
(fma.f32 (/.f32 (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)) maxCos) (+.f32 -1 (/.f32 1 ux)) (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)))
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 1 (+.f32 (.f32 (-.f32 maxCos 1) ux) (.f32 (+.f32 (.f32 1/2 (pow.f32 (-.f32 maxCos 1) 2)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 2))) (pow.f32 ux 2))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 1 (+.f32 (.f32 (+.f32 (.f32 1/6 (pow.f32 (-.f32 maxCos 1) 3)) (+.f32 (.f32 1/3 (pow.f32 (-.f32 maxCos 1) 3)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 3)))) (pow.f32 ux 3)) (+.f32 (.f32 (-.f32 maxCos 1) ux) (.f32 (+.f32 (.f32 1/2 (pow.f32 (-.f32 maxCos 1) 2)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 2))) (pow.f32 ux 2)))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux)))))
(*.f32 ux (+.f32 -1 maxCos))
(-.f32 (*.f32 ux maxCos) ux)
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1)))))
(exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1)))))
(*.f32 (pow.f32 (/.f32 -1 ux) -1) (+.f32 (neg.f32 maxCos) 1))
(/.f32 (+.f32 1 (neg.f32 maxCos)) (/.f32 -1 ux))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (*.f32 ux (+.f32 maxCos -1))))
(fma.f32 (pow.f32 (/.f32 -1 ux) -1) (+.f32 (neg.f32 maxCos) 1) (*.f32 (/.f32 (pow.f32 (/.f32 -1 ux) -1) ux) (/.f32 (+.f32 (neg.f32 maxCos) 1) (+.f32 -1 maxCos))))
(+.f32 (/.f32 (+.f32 1 (neg.f32 maxCos)) (/.f32 -1 ux)) (*.f32 (/.f32 (/.f32 1 (/.f32 -1 ux)) ux) -1))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (*.f32 ux (+.f32 maxCos -1))))
(fma.f32 (pow.f32 (/.f32 -1 ux) -1) (+.f32 (neg.f32 maxCos) 1) (*.f32 (/.f32 (pow.f32 (/.f32 -1 ux) -1) ux) (/.f32 (+.f32 (neg.f32 maxCos) 1) (+.f32 -1 maxCos))))
(+.f32 (/.f32 (+.f32 1 (neg.f32 maxCos)) (/.f32 -1 ux)) (*.f32 (/.f32 (/.f32 1 (/.f32 -1 ux)) ux) -1))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (*.f32 ux (+.f32 maxCos -1))))
(fma.f32 (pow.f32 (/.f32 -1 ux) -1) (+.f32 (neg.f32 maxCos) 1) (*.f32 (/.f32 (pow.f32 (/.f32 -1 ux) -1) ux) (/.f32 (+.f32 (neg.f32 maxCos) 1) (+.f32 -1 maxCos))))
(+.f32 (/.f32 (+.f32 1 (neg.f32 maxCos)) (/.f32 -1 ux)) (*.f32 (/.f32 (/.f32 1 (/.f32 -1 ux)) ux) -1))

prune120.0ms (5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	148	2	150

Error

Counts

150 → 2

Alt Table

Status	Error	Program
▶	0.0b	(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
✓	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))

Compiler

Compiled 3053 to 2327 computations (23.8% saved)

localize26.0ms (1.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
	0.0b	(log1p.f32 (*.f32 (+.f32 maxCos -1) ux))
	0.1b	(*.f32 (+.f32 maxCos -1) ux)

series16.0ms (0.7%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	ux	@	inf	(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
6.0ms	ux	@	-inf	(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
1.0ms	maxCos	@	0	(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
1.0ms	maxCos	@	inf	(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
1.0ms	maxCos	@	-inf	(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))

rewrite37.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

838×	`expm1-log1p-u_binary32`
837×	`log1p-expm1-u_binary32`
95×	`add-sqr-sqrt_binary32`
92×	`pow1_binary32`
91×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	195	10
2	2264	10

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 1 (*.f32 (+.f32 maxCos -1) ux))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (+.f32 maxCos -1) ux) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux))) (cbrt.f32 (pow.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)) 2)) (cbrt.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux))) (sqrt.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 1 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) (pow.f32 (cbrt.f32 (E.f32)) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (E.f32)) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))) (pow.f32 (sqrt.f32 (E.f32)) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 3)) (+.f32 1 (-.f32 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2) (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 (*.f32 (+.f32 maxCos -1) ux) 2)) (-.f32 1 (*.f32 (+.f32 maxCos -1) ux)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (+.f32 1 (*.f32 (+.f32 maxCos -1) ux))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))))))

simplify29.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

792×	`times-frac_binary32`
784×	`fma-def_binary32`
505×	`distribute-rgt-in_binary32`
110×	`distribute-rgt-out_binary32`
90×	`associate-r_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	763
1	450	594
2	1784	382

Stop Event

1×	node limit

Counts

44 → 51

Calls

Call 1

Inputs
(+.f32 (*.f32 -1 ux) 1)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (.f32 -1 ux) (+.f32 1 (+.f32 (.f32 maxCos ux) (.f32 (+.f32 (.f32 1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (.f32 -1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)))) (.f32 (pow.f32 maxCos 2) (+.f32 (*.f32 -1 ux) 1))))))
(+.f32 (.f32 (pow.f32 maxCos 3) (.f32 (+.f32 (.f32 1/3 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (+.f32 (.f32 1/6 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (.f32 -1/2 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))))) (+.f32 (.f32 -1 ux) 1))) (+.f32 (.f32 -1 ux) (+.f32 1 (+.f32 (.f32 maxCos ux) (.f32 (+.f32 (.f32 1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (.f32 -1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)))) (.f32 (pow.f32 maxCos 2) (+.f32 (.f32 -1 ux) 1)))))))
(exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (pow.f32 (-.f32 (/.f32 1 ux) 1) 2))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) (pow.f32 maxCos 2))))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)) (pow.f32 ux 2))) (+.f32 (.f32 1/6 (pow.f32 (-.f32 (/.f32 1 ux) 1) 3)) (.f32 1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) (pow.f32 maxCos 3)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos) (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (pow.f32 (-.f32 (/.f32 1 ux) 1) 2)))) (pow.f32 maxCos 2)))))
(exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))
(+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (*.f32 -1 ux)))))
(+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))))) (pow.f32 maxCos 2)) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 (.f32 -1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))) (.f32 -1/6 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))) (pow.f32 maxCos 3))) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))) (pow.f32 maxCos 2)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))))))
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 1 (+.f32 (.f32 (-.f32 maxCos 1) ux) (.f32 (+.f32 (.f32 1/2 (pow.f32 (-.f32 maxCos 1) 2)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 2))) (pow.f32 ux 2))))
(+.f32 1 (+.f32 (.f32 (+.f32 (.f32 1/6 (pow.f32 (-.f32 maxCos 1) 3)) (+.f32 (.f32 1/3 (pow.f32 (-.f32 maxCos 1) 3)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 3)))) (pow.f32 ux 3)) (+.f32 (.f32 (-.f32 maxCos 1) ux) (.f32 (+.f32 (.f32 1/2 (pow.f32 (-.f32 maxCos 1) 2)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 2))) (pow.f32 ux 2)))))
(exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux)))))
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1)))))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))

Outputs
(+.f32 (*.f32 -1 ux) 1)
(fma.f32 -1 ux 1)
(-.f32 1 ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (.f32 maxCos ux)))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (.f32 -1 ux) (+.f32 1 (+.f32 (.f32 maxCos ux) (.f32 (+.f32 (.f32 1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (.f32 -1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)))) (.f32 (pow.f32 maxCos 2) (+.f32 (*.f32 -1 ux) 1))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (.f32 (pow.f32 maxCos 3) (.f32 (+.f32 (.f32 1/3 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (+.f32 (.f32 1/6 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))) (.f32 -1/2 (/.f32 (pow.f32 ux 3) (pow.f32 (+.f32 (.f32 -1 ux) 1) 3))))) (+.f32 (.f32 -1 ux) 1))) (+.f32 (.f32 -1 ux) (+.f32 1 (+.f32 (.f32 maxCos ux) (.f32 (+.f32 (.f32 1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2))) (.f32 -1/2 (/.f32 (pow.f32 ux 2) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)))) (.f32 (pow.f32 maxCos 2) (+.f32 (.f32 -1 ux) 1)))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))
(exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux)))
(*.f32 ux (exp.f32 (log.f32 maxCos)))
(*.f32 ux maxCos)
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos))
(+.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))) (/.f32 (+.f32 (/.f32 1 ux) -1) (/.f32 maxCos (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))))
(fma.f32 (exp.f32 (log.f32 maxCos)) ux (.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) (.f32 ux (exp.f32 (log.f32 maxCos)))))
(.f32 (+.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) 1) (.f32 ux maxCos))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos) (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (pow.f32 (-.f32 (/.f32 1 ux) 1) 2))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) (pow.f32 maxCos 2))))
(+.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))) (+.f32 (/.f32 (+.f32 (/.f32 1 ux) -1) (/.f32 maxCos (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))) (/.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))) (/.f32 (.f32 maxCos maxCos) (fma.f32 -1/2 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 2) (.f32 ux ux)) (*.f32 1/2 (pow.f32 (+.f32 (/.f32 1 ux) -1) 2)))))))
(+.f32 (fma.f32 (exp.f32 (log.f32 maxCos)) ux (.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) (.f32 ux (exp.f32 (log.f32 maxCos))))) (.f32 (/.f32 (.f32 ux (exp.f32 (log.f32 maxCos))) (.f32 maxCos maxCos)) (fma.f32 -1/2 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux ux)) (*.f32 1/2 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 2)))))
(fma.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) (*.f32 ux maxCos) (fma.f32 ux maxCos 0))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (pow.f32 (+.f32 (.f32 -1 ux) 1) 2)) (pow.f32 ux 2))) (+.f32 (.f32 1/6 (pow.f32 (-.f32 (/.f32 1 ux) 1) 3)) (.f32 1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) (pow.f32 maxCos 3)) (+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (/.f32 (.f32 (-.f32 (/.f32 1 ux) 1) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux)))) maxCos) (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 maxCos))) (log.f32 ux))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (pow.f32 (-.f32 (/.f32 1 ux) 1) 2)))) (pow.f32 maxCos 2)))))
(+.f32 (/.f32 (fma.f32 -1/2 (/.f32 (+.f32 (/.f32 1 ux) -1) (/.f32 (.f32 ux ux) (pow.f32 (fma.f32 -1 ux 1) 2))) (fma.f32 1/6 (pow.f32 (+.f32 (/.f32 1 ux) -1) 3) (.f32 1/3 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 3) (pow.f32 ux 3))))) (/.f32 (pow.f32 maxCos 3) (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))) (+.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))) (+.f32 (/.f32 (+.f32 (/.f32 1 ux) -1) (/.f32 maxCos (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))))) (/.f32 (exp.f32 (fma.f32 -1 (neg.f32 (log.f32 maxCos)) (log.f32 ux))) (/.f32 (.f32 maxCos maxCos) (fma.f32 -1/2 (/.f32 (pow.f32 (fma.f32 -1 ux 1) 2) (.f32 ux ux)) (*.f32 1/2 (pow.f32 (+.f32 (/.f32 1 ux) -1) 2))))))))
(+.f32 (.f32 (/.f32 (fma.f32 -1/2 (.f32 (/.f32 (pow.f32 (-.f32 1 ux) 2) ux) (/.f32 (+.f32 -1 (/.f32 1 ux)) ux)) (fma.f32 1/3 (/.f32 (pow.f32 (-.f32 1 ux) 3) (pow.f32 ux 3)) (.f32 1/6 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 3)))) (pow.f32 maxCos 3)) (.f32 ux (exp.f32 (log.f32 maxCos)))) (+.f32 (fma.f32 (exp.f32 (log.f32 maxCos)) ux (.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) (.f32 ux (exp.f32 (log.f32 maxCos))))) (.f32 (/.f32 (.f32 ux (exp.f32 (log.f32 maxCos))) (.f32 maxCos maxCos)) (fma.f32 -1/2 (/.f32 (pow.f32 (-.f32 1 ux) 2) (.f32 ux ux)) (*.f32 1/2 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 2))))))
(fma.f32 (/.f32 (fma.f32 -1/2 (/.f32 (+.f32 -1 (/.f32 1 ux)) (/.f32 ux (/.f32 (pow.f32 (-.f32 1 ux) 2) ux))) (fma.f32 1/2 (pow.f32 (+.f32 -1 (/.f32 1 ux)) 3) 0)) (pow.f32 maxCos 3)) (.f32 ux maxCos) (fma.f32 (/.f32 (+.f32 -1 (/.f32 1 ux)) maxCos) (.f32 ux maxCos) (fma.f32 ux maxCos 0)))
(exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))
(exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux))))
(*.f32 (neg.f32 ux) (pow.f32 (/.f32 -1 maxCos) -1))
(/.f32 (neg.f32 ux) (/.f32 -1 maxCos))
(+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (*.f32 -1 ux)))))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (*.f32 (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) maxCos) (/.f32 (fma.f32 -1 ux 1) ux)))
(fma.f32 (pow.f32 (/.f32 -1 maxCos) -1) (neg.f32 ux) (*.f32 (/.f32 (pow.f32 (/.f32 -1 maxCos) -1) (/.f32 maxCos (neg.f32 ux))) (/.f32 (-.f32 1 ux) ux)))
(fma.f32 (/.f32 (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)) ux) (/.f32 (-.f32 1 ux) maxCos) (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)))
(+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))))) (pow.f32 maxCos 2)) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (*.f32 (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) maxCos) (/.f32 (fma.f32 -1 ux 1) ux)))
(fma.f32 (pow.f32 (/.f32 -1 maxCos) -1) (neg.f32 ux) (*.f32 (/.f32 (pow.f32 (/.f32 -1 maxCos) -1) (/.f32 maxCos (neg.f32 ux))) (/.f32 (-.f32 1 ux) ux)))
(fma.f32 (/.f32 (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)) ux) (/.f32 (-.f32 1 ux) maxCos) (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 (.f32 -1/3 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))) (.f32 -1/6 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 3) (pow.f32 ux 3))))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))) (pow.f32 maxCos 3))) (+.f32 (/.f32 (.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))) (+.f32 (.f32 -1 ux) 1)) (.f32 maxCos ux)) (+.f32 (/.f32 (.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 -1 ux) 1) 2) (pow.f32 ux 2)))) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux))))) (pow.f32 maxCos 2)) (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 maxCos))) (log.f32 (.f32 -1 ux)))))))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) (*.f32 (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 maxCos)) (log.f32 (neg.f32 ux)))) maxCos) (/.f32 (fma.f32 -1 ux 1) ux)))
(fma.f32 (pow.f32 (/.f32 -1 maxCos) -1) (neg.f32 ux) (*.f32 (/.f32 (pow.f32 (/.f32 -1 maxCos) -1) (/.f32 maxCos (neg.f32 ux))) (/.f32 (-.f32 1 ux) ux)))
(fma.f32 (/.f32 (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)) ux) (/.f32 (-.f32 1 ux) maxCos) (/.f32 (neg.f32 ux) (/.f32 -1 maxCos)))
1
(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 1 (+.f32 (.f32 (-.f32 maxCos 1) ux) (.f32 (+.f32 (.f32 1/2 (pow.f32 (-.f32 maxCos 1) 2)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 2))) (pow.f32 ux 2))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 1 (+.f32 (.f32 (+.f32 (.f32 1/6 (pow.f32 (-.f32 maxCos 1) 3)) (+.f32 (.f32 1/3 (pow.f32 (-.f32 maxCos 1) 3)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 3)))) (pow.f32 ux 3)) (+.f32 (.f32 (-.f32 maxCos 1) ux) (.f32 (+.f32 (.f32 1/2 (pow.f32 (-.f32 maxCos 1) 2)) (.f32 -1/2 (pow.f32 (-.f32 maxCos 1) 2))) (pow.f32 ux 2)))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux)))))
(exp.f32 (+.f32 (log.f32 (+.f32 maxCos -1)) (neg.f32 (neg.f32 (log.f32 ux)))))
(*.f32 ux (+.f32 -1 maxCos))
(fma.f32 ux maxCos (neg.f32 ux))
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(+.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (.f32 -1 (log.f32 (/.f32 1 ux))))) (.f32 (-.f32 maxCos 1) ux)) (exp.f32 (+.f32 (log.f32 (-.f32 maxCos 1)) (*.f32 -1 (log.f32 (/.f32 1 ux))))))
(+.f32 (fma.f32 -1 ux 1) (*.f32 ux maxCos))
(-.f32 (fma.f32 ux maxCos 1) ux)
(exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1)))))
(exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1)))))
(*.f32 (pow.f32 (/.f32 -1 ux) -1) (+.f32 (neg.f32 maxCos) 1))
(/.f32 (fma.f32 -1 maxCos 1) (/.f32 -1 ux))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (*.f32 ux (+.f32 maxCos -1))))
(fma.f32 (pow.f32 (/.f32 -1 ux) -1) (+.f32 (neg.f32 maxCos) 1) (*.f32 (/.f32 (pow.f32 (/.f32 -1 ux) -1) ux) (/.f32 (+.f32 (neg.f32 maxCos) 1) (+.f32 -1 maxCos))))
(fma.f32 (/.f32 (/.f32 1 (/.f32 -1 ux)) ux) -1 (/.f32 (fma.f32 -1 maxCos 1) (/.f32 -1 ux)))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (*.f32 ux (+.f32 maxCos -1))))
(fma.f32 (pow.f32 (/.f32 -1 ux) -1) (+.f32 (neg.f32 maxCos) 1) (*.f32 (/.f32 (pow.f32 (/.f32 -1 ux) -1) ux) (/.f32 (+.f32 (neg.f32 maxCos) 1) (+.f32 -1 maxCos))))
(fma.f32 (/.f32 (/.f32 1 (/.f32 -1 ux)) ux) -1 (/.f32 (fma.f32 -1 maxCos 1) (/.f32 -1 ux)))
(+.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (/.f32 (exp.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 -1 ux))) (log.f32 (.f32 -1 (-.f32 maxCos 1))))) (*.f32 (-.f32 maxCos 1) ux)))
(+.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (/.f32 (exp.f32 (fma.f32 -1 (log.f32 (/.f32 -1 ux)) (log.f32 (neg.f32 (+.f32 maxCos -1))))) (*.f32 ux (+.f32 maxCos -1))))
(fma.f32 (pow.f32 (/.f32 -1 ux) -1) (+.f32 (neg.f32 maxCos) 1) (*.f32 (/.f32 (pow.f32 (/.f32 -1 ux) -1) ux) (/.f32 (+.f32 (neg.f32 maxCos) 1) (+.f32 -1 maxCos))))
(fma.f32 (/.f32 (/.f32 1 (/.f32 -1 ux)) ux) -1 (/.f32 (fma.f32 -1 maxCos 1) (/.f32 -1 ux)))

prune104.0ms (4.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	145	2	147

Error

Counts

147 → 2

Alt Table

Status	Error	Program
✓	0.0b	(pow.f32 (exp.f32 1) (log1p.f32 (*.f32 (+.f32 maxCos -1) ux)))
✓	0.0b	(+.f32 1 (*.f32 (-.f32 maxCos 1) ux))

Compiler

Compiled 3213 to 2482 computations (22.8% saved)

regimes61.0ms (2.5%)

Accuracy

Total -0.0b remaining (-103.6%)

Threshold costs -0.0b (-103.6%)

Counts

23 → 1

Compiler

Compiled 263 to 175 computations (33.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	10	8

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f32 (+.f32 maxCos -1) ux 1)

Outputs
(fma.f32 (+.f32 maxCos -1) ux 1)

end26.0ms (1.1%)

Stop Event

1×

done

Compiler

Compiled 34 to 26 computations (23.5% saved)

Iter	Nodes	Cost
0	13	201
1	31	173
2	46	173
3	64	173
4	96	173
5	155	173
6	311	173
7	522	173
8	733	173
9	822	173
10	846	173
11	847	173

Iter	Nodes	Cost
0	13	201
1	31	173
2	46	173
3	64	173
4	96	173
5	155	173
6	311	173
7	522	173
8	733	173
9	822	173
10	846	173
11	847	173

Details

analyze1.0ms (0%)

sample1.5s (62.9%)

preprocess38.0ms (1.6%)

simplify14.0ms (0.6%)

prune3.0ms (0.1%)

localize15.0ms (0.6%)

series3.0ms (0.1%)

rewrite36.0ms (1.5%)

simplify19.0ms (0.8%)

prune45.0ms (1.9%)

localize17.0ms (0.7%)

series5.0ms (0.2%)

rewrite38.0ms (1.6%)

simplify24.0ms (1%)

prune59.0ms (2.5%)

localize19.0ms (0.8%)

series39.0ms (1.6%)

rewrite41.0ms (1.7%)

simplify48.0ms (2%)

prune120.0ms (5%)

localize26.0ms (1.1%)

series16.0ms (0.7%)

rewrite37.0ms (1.5%)

simplify29.0ms (1.2%)

prune104.0ms (4.4%)

regimes61.0ms (2.5%)

simplify2.0ms (0.1%)

end26.0ms (1.1%)

Profiling

Iter	Nodes	Cost
0	13	201
1	31	173
2	46	173
3	64	173
4	96	173
5	155	173
6	311	173
7	522	173
8	733	173
9	822	173
10	846	173
11	847	173