Details

analyze631.0ms (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0%	0.1%	99.9%	1
0%	0.1%	99.9%	2
0%	0.1%	99.9%	3
0%	0%	99.9%	4
0%	0%	99.9%	5
0%	0%	99.9%	6
0.1%	0%	99.9%	7
0.1%	0%	99.9%	8
0.1%	0%	99.9%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 51 to 37 computations (27.5% saved)

sample2.6s (20.1%)

Results

2.5s

8256×

body

128

valid

Compiler

Compiled 130 to 94 computations (27.7% saved)

simplify49.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

743×	`sub-neg_binary32`
674×	`fma-neg_binary32`
386×	`associate--l-_binary32`
316×	`distribute-rgt-in_binary32`
286×	`unsub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	41	35
2	117	35
3	431	33
4	1755	33
5	4135	33
6	4966	33

prune5.0ms (0%)

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

12.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.0b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	13.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))

Status

Error

Program

▶

13.0b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))

13.1b

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (*.f32 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))))

Compiler

Compiled 156 to 110 computations (29.5% saved)

localize54.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.3b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
✓	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	13.6b	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

series306.0ms (2.3%)

Counts

4 → 80

Calls

4 calls:

284.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
15.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)
4.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
3.0ms	(.f32 (.f32 uy 2) (PI.f32))

rewrite76.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

316×	`expm1-udef_binary32`
315×	`log1p-udef_binary32`
177×	`add-sqr-sqrt_binary32`
166×	`log1p-expm1-u_binary32`
166×	`expm1-log1p-u_binary32`

Counts

4 → 76

Calls

4 calls:

74.0ms	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
74.0ms	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
74.0ms	(.f32 (.f32 uy 2) (PI.f32))
73.0ms	(fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	353	70
2	4246	70
3	5106	70
0	0	0
1	0	0

simplify125.0ms (1%)

Algorithm

1×	egg-herbie

Rules

491×	`fma-neg_binary32`
355×	`fma-def_binary32`
341×	`sub-neg_binary32`
288×	`associate-r_binary32`
275×	`associate-l_binary32`

Counts

156 → 148

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	292	6087
1	1011	5248
2	4149	5248
3	4989	5248

prune235.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	138	10	148
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	139	11	150

Error

0.3b

Counts

150 → 11

Alt Table

Status	Error	Program
	13.5b	(sqrt.f32 (.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1) (pow.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) 2)))
	1.1b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	13.0b	(.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (pow.f32 (cbrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)) 3)))
	1.1b	(-.f32 (+.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))) (.f32 (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))) (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos (pow.f32 ux 2))))) (.f32 (sqrt.f32 (/.f32 1 (-.f32 (.f32 2 ux) (pow.f32 ux 2)))) (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (.f32 maxCos ux))))
	13.7b	(.f32 (exp.f32 (log.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))
	13.1b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (fma.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (-.f32 ux (fma.f32 ux maxCos 1)) 1)))) 3)
▶	0.5b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	1.9b	(-.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5))))) (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 4/3 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 8/315 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7))))))
	2.5b	(fma.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
	13.1b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
	8.0b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (.f32 (-.f32 2 (*.f32 2 maxCos)) ux)))

Compiler

Compiled 9286 to 6119 computations (34.1% saved)

localize72.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux)))
	0.2b	(sin.f32 (.f32 (.f32 uy 2) (PI.f32)))
✓	0.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))

series302.0ms (2.3%)

Counts

2 → 56

Calls

2 calls:

289.0ms

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (+.f32 (*.f32 2 (*.f32 maxCos ux)) (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))

13.0ms

(+.f32 (*.f32 2 (*.f32 maxCos ux)) (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux)))

rewrite69.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

765×	`prod-diff_binary32`
217×	`add-sqr-sqrt_binary32`
205×	`log1p-expm1-u_binary32`
205×	`expm1-log1p-u_binary32`
201×	`add-log-exp_binary32`

Counts

2 → 54

Calls

2 calls:

67.0ms

(+.f32 (*.f32 2 (*.f32 maxCos ux)) (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux)))

67.0ms

(*.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (+.f32 (*.f32 2 (*.f32 maxCos ux)) (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	63
1	440	63
2	4797	63
3	6071	63
0	0	0
1	0	0

simplify142.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-neg_binary32`
320×	`fma-def_binary32`
311×	`sub-neg_binary32`
298×	`associate-r_binary32`
243×	`associate-l_binary32`

Counts

110 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	278	5502
1	936	4762
2	3947	4762
3	4999	4762
4	5062	4762

prune396.0ms (3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	146	13	159
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	155	15	170

Error

0.1b

Counts

170 → 15

Alt Table

Status	Error	Program
	0.9b	(.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
▶	0.5b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	3.2b	(.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (log.f32 (exp.f32 (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))))
	1.1b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	1.8b	(.f32 (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 2) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	2.5b	(fma.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
	2.6b	(.f32 (exp.f32 (log.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	3.0b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))))
	0.7b	(.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 2)) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	1.8b	(pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 2)
	0.9b	(.f32 (.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 2) (cbrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))))
	0.9b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 3)
	3.5b	(pow.f32 (pow.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))))) 3) 1/3)
	0.5b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))

Compiler

Compiled 10833 to 6552 computations (39.5% saved)

localize82.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))
✓	0.4b	(pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)
✓	0.7b	(pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)

series1.7s (12.7%)

Counts

3 → 68

Calls

3 calls:

1.5s

(*.f32 (pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))

181.0ms

(pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)

15.0ms

(pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3)

rewrite71.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

319×	`prod-diff_binary32`
226×	`add-sqr-sqrt_binary32`
216×	`log1p-expm1-u_binary32`
216×	`expm1-log1p-u_binary32`
211×	`add-cbrt-cube_binary32`

Counts

3 → 45

Calls

3 calls:

69.0ms

(*.f32 (pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3) (pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))

69.0ms

(pow.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (fma.f32 2 (*.f32 maxCos ux) (*.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)

69.0ms

(pow.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	96
1	475	96
2	4749	96
3	5277	96
0	0	0
1	0	0

simplify310.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

463×	`*-commutative_binary32`
403×	`times-frac_binary32`
290×	`+-commutative_binary32`
274×	`fma-def_binary32`
236×	`associate-+r+_binary32`

Counts

113 → 150

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1045	19397
1	3671	18917
2	5214	18917

prune691.0ms (5.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	157	9	166
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	164	17	181

Error

0.0b

Counts

181 → 17

Alt Table

Status	Error	Program
	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	1.1b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	27.7b	(cbrt.f32 (log.f32 (pow.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))))
	5.8b	(cbrt.f32 (.f32 8 (.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (sqrt.f32 (pow.f32 (-.f32 (.f32 2 (+.f32 (.f32 (.f32 ux ux) maxCos) ux)) (+.f32 (.f32 ux ux) (fma.f32 (.f32 maxCos maxCos) (.f32 ux ux) (.f32 2 (*.f32 ux maxCos))))) 3)))))
	4.4b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (+.f32 (fma.f32 3 (/.f32 (.f32 maxCos (.f32 ux (exp.f32 (.f32 3/2 (+.f32 (log.f32 (-.f32 2 (.f32 2 maxCos))) (log.f32 ux)))))) (-.f32 2 (.f32 2 maxCos))) (exp.f32 (.f32 3/2 (+.f32 (log.f32 (-.f32 2 (.f32 2 maxCos))) (log.f32 ux))))) (.f32 -3/2 (+.f32 (/.f32 (.f32 (.f32 maxCos maxCos) (.f32 ux (exp.f32 (.f32 3/2 (+.f32 (log.f32 (-.f32 2 (.f32 2 maxCos))) (log.f32 ux)))))) (-.f32 2 (.f32 2 maxCos))) (/.f32 (.f32 ux (exp.f32 (.f32 3/2 (+.f32 (log.f32 (-.f32 2 (.f32 2 maxCos))) (log.f32 ux))))) (-.f32 2 (*.f32 2 maxCos))))))))
	2.5b	(fma.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
▶	0.5b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.9b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	2.6b	(.f32 (exp.f32 (log.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	3.0b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))))
	22.1b	(cbrt.f32 (.f32 (log.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	2.5b	(cbrt.f32 (.f32 (-.f32 (fma.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 208/15 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))) (fma.f32 1312/189 (.f32 (pow.f32 uy 9) (pow.f32 (PI.f32) 9)) (.f32 16 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))))) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.8b	(cbrt.f32 (.f32 (.f32 (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.6b	(cbrt.f32 (.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3/2) (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3/2)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.6b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (.f32 uy 2) (PI.f32))))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.8b	(pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 2)
	0.9b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 3)

Compiler

Compiled 29200 to 20845 computations (28.6% saved)

localize82.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f32 (expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))))
✓	0.2b	(expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))
✓	0.3b	(.f32 (log1p.f32 (expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	0.4b	(.f32 (.f32 uy 2) (PI.f32))

series357.0ms (2.7%)

Counts

3 → 56

Calls

3 calls:

347.0ms

(*.f32 (log1p.f32 (expm1.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (+.f32 (*.f32 2 (*.f32 maxCos ux)) (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))

6.0ms

(expm1.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))))

4.0ms

(log1p.f32 (expm1.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32)))))

rewrite74.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

398×	`prod-diff_binary32`
225×	`add-sqr-sqrt_binary32`
215×	`expm1-log1p-u_binary32`
214×	`log1p-expm1-u_binary32`
208×	`add-log-exp_binary32`

Counts

3 → 46

Calls

3 calls:

73.0ms

(log1p.f32 (expm1.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32)))))

73.0ms

(expm1.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))))

73.0ms

(*.f32 (log1p.f32 (expm1.f32 (sin.f32 (*.f32 (*.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (*.f32 2 (fma.f32 maxCos (*.f32 ux ux) ux)) (+.f32 (*.f32 2 (*.f32 maxCos ux)) (*.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	67
1	459	67
2	4853	67
3	5386	67
0	0	0
1	0	0

simplify139.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

507×	`fma-neg_binary32`
364×	`fma-def_binary32`
338×	`sub-neg_binary32`
325×	`associate-r_binary32`
266×	`associate-l_binary32`

Counts

102 → 113

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	300	5468
1	1019	4758
2	4238	4758
3	5129	4758

prune274.0ms (2.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	129	17	146

Error

0.0b

Counts

146 → 17

Alt Table

Status	Error	Program
	0.5b	(.f32 (sin.f32 (expm1.f32 (log1p.f32 (.f32 (.f32 uy 2) (PI.f32))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	1.1b	(fma.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (.f32 ux (-.f32 2 ux))) (.f32 (.f32 (sin.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (/.f32 1 (.f32 ux (-.f32 2 ux))))) (-.f32 (.f32 maxCos (.f32 ux ux)) (*.f32 maxCos ux))))
	27.7b	(cbrt.f32 (log.f32 (pow.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2))))
	5.8b	(cbrt.f32 (.f32 8 (.f32 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (sqrt.f32 (pow.f32 (-.f32 (.f32 2 (+.f32 (.f32 (.f32 ux ux) maxCos) ux)) (+.f32 (.f32 ux ux) (fma.f32 (.f32 maxCos maxCos) (.f32 ux ux) (.f32 2 (*.f32 ux maxCos))))) 3)))))
	4.4b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3) (+.f32 (fma.f32 3 (/.f32 (.f32 maxCos (.f32 ux (exp.f32 (.f32 3/2 (+.f32 (log.f32 (-.f32 2 (.f32 2 maxCos))) (log.f32 ux)))))) (-.f32 2 (.f32 2 maxCos))) (exp.f32 (.f32 3/2 (+.f32 (log.f32 (-.f32 2 (.f32 2 maxCos))) (log.f32 ux))))) (.f32 -3/2 (+.f32 (/.f32 (.f32 (.f32 maxCos maxCos) (.f32 ux (exp.f32 (.f32 3/2 (+.f32 (log.f32 (-.f32 2 (.f32 2 maxCos))) (log.f32 ux)))))) (-.f32 2 (.f32 2 maxCos))) (/.f32 (.f32 ux (exp.f32 (.f32 3/2 (+.f32 (log.f32 (-.f32 2 (.f32 2 maxCos))) (log.f32 ux))))) (-.f32 2 (*.f32 2 maxCos))))))))
	2.5b	(fma.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (fma.f32 2 (.f32 uy (PI.f32)) (.f32 4/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5)))) (.f32 (.f32 (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (.f32 ux ux))))) (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3))) -4/3))
	0.9b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 uy 2) (PI.f32))) 3)) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	0.5b	(.f32 (log1p.f32 (log1p.f32 (expm1.f32 (expm1.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	22.1b	(cbrt.f32 (.f32 (log.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3))) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	2.5b	(cbrt.f32 (.f32 (-.f32 (fma.f32 8 (.f32 (pow.f32 uy 3) (pow.f32 (PI.f32) 3)) (.f32 208/15 (.f32 (pow.f32 uy 7) (pow.f32 (PI.f32) 7)))) (fma.f32 1312/189 (.f32 (pow.f32 uy 9) (pow.f32 (PI.f32) 9)) (.f32 16 (.f32 (pow.f32 uy 5) (pow.f32 (PI.f32) 5))))) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.8b	(cbrt.f32 (.f32 (.f32 (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3) (pow.f32 (sqrt.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32)))) 3)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.6b	(cbrt.f32 (.f32 (.f32 (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3/2) (pow.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) 3/2)) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (*.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.6b	(cbrt.f32 (.f32 (pow.f32 (sin.f32 (exp.f32 (log.f32 (.f32 (.f32 uy 2) (PI.f32))))) 3) (pow.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1)))) 3/2)))
	1.8b	(pow.f32 (sqrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 2)
	0.9b	(pow.f32 (cbrt.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))) 3)
	3.2b	(.f32 (log1p.f32 (+.f32 (.f32 2 (-.f32 (fma.f32 (PI.f32) uy (.f32 (.f32 uy uy) (pow.f32 (PI.f32) 2))) (.f32 (pow.f32 uy 4) (pow.f32 (PI.f32) 4)))) (.f32 -32/15 (.f32 (pow.f32 (PI.f32) 5) (pow.f32 uy 5))))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (+.f32 (.f32 2 (.f32 maxCos ux)) (.f32 (fma.f32 maxCos maxCos 1) (*.f32 ux ux))))))
	3.0b	(exp.f32 (log.f32 (.f32 (sin.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 (.f32 2 (fma.f32 maxCos (.f32 ux ux) ux)) (fma.f32 2 (.f32 maxCos ux) (.f32 (.f32 ux ux) (fma.f32 maxCos maxCos 1))))))))

Compiler

Compiled 9416 to 5839 computations (38% saved)

regimes3.8s (29.1%)

Accuracy

Total 0.5b remaining (82.8%)

Threshold costs 0.5b (82.8%)

Counts

203 → 1

Compiler

Compiled 101719 to 71753 computations (29.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary32`
10×	`+-commutative_binary32`
9×	`sub-neg_binary32`
8×	`neg-sub0_binary32`
8×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	55
1	37	55
2	45	55
3	66	55
4	85	55
5	97	55
6	104	55
7	106	55
8	104	55

end439.0ms (3.4%)

Compiler: Compiled 892 to 616 computations (30.9% saved)

Details

analyze631.0ms (4.8%)

sample2.6s (20.1%)

simplify49.0ms (0.4%)

prune5.0ms (0%)

localize54.0ms (0.4%)

series306.0ms (2.3%)

rewrite76.0ms (0.6%)

simplify125.0ms (1%)

prune235.0ms (1.8%)

localize72.0ms (0.6%)

series302.0ms (2.3%)

rewrite69.0ms (0.5%)

simplify142.0ms (1.1%)

prune396.0ms (3%)

localize82.0ms (0.6%)

series1.7s (12.7%)

rewrite71.0ms (0.5%)

simplify310.0ms (2.4%)

prune691.0ms (5.3%)

localize82.0ms (0.6%)

series357.0ms (2.7%)

rewrite74.0ms (0.6%)

simplify139.0ms (1.1%)

prune274.0ms (2.1%)

regimes3.8s (29.1%)

simplify4.0ms (0%)

end439.0ms (3.4%)

Profiling