Details

analyze409.0ms (3.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 39 to 31 computations (20.5% saved)

sample2.2s (18.4%)

Results

2.1s	8256×	body	128	valid
2.0ms	7×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

40×	`fma-neg_binary32`
22×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
13×	`fma-def_binary32`
10×	`*-commutative_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

Compiler

Compiled 58 to 49 computations (15.5% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓	0.1b	(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
✓	0.1b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
✓	0.3b	(*.f32 (PI.f32) u2)

series145.0ms (1.2%)

Counts

4 → 32

Calls

4 calls:

132.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
8.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
2.0ms	(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
2.0ms	(*.f32 (PI.f32) u2)

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`prod-diff_binary32`
204×	`expm1-udef_binary32`
204×	`log1p-udef_binary32`
132×	`add-sqr-sqrt_binary32`
124×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	266	37
2	3275	37

Stop Event

1×	node limit

Counts

4 → 96

Calls

4 calls:

50.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
50.0ms	(cos.f32 (.f32 2 (.f32 (PI.f32) u2)))
50.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
50.0ms	(*.f32 (PI.f32) u2)

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

538×	`cancel-sign-sub-inv_binary32`
348×	`times-frac_binary32`
276×	`associate-*l/_binary32`
247×	`associate-/r*_binary32`
218×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	1948
1	571	1783
2	2097	1637

Stop Event

1×	node limit

Counts

128 → 144

prune217.0ms (1.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	131	13	144
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	14	145

Error

0.0b

Counts

145 → 14

Alt Table

Status	Error	Program
	8.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 u1) 3/2)) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	1.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 3) 1/3))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (-.f32 (pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) 3) (pow.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 3)) (+.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (+.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	12.1b	(.f32 (-.f32 (exp.f32 (log1p.f32 (sqrt.f32 (log1p.f32 u1)))) 1) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
	8.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))))

Compiler

Compiled 5523 to 3427 computations (38% saved)

localize47.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
✓	0.2b	(log1p.f32 (*.f32 (PI.f32) u2))
	0.3b	(*.f32 (PI.f32) u2)
✓	13.7b	(-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1)

series562.0ms (4.8%)

Counts

3 → 44

Calls

3 calls:

517.0ms

(-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1)

39.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))

6.0ms

(log1p.f32 (*.f32 (PI.f32) u2))

rewrite54.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

994×	`prod-diff_binary32`
156×	`add-sqr-sqrt_binary32`
150×	`expm1-log1p-u_binary32`
148×	`log1p-expm1-u_binary32`
144×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	33
1	329	29
2	3962	29

Stop Event

1×	node limit

Counts

3 → 79

Calls

3 calls:

52.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (*.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))

52.0ms

(log1p.f32 (*.f32 (PI.f32) u2))

52.0ms

(-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1)

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

839×	`fma-def_binary32`
565×	`cancel-sign-sub-inv_binary32`
199×	`fma-neg_binary32`
174×	`sub-neg_binary32`
161×	`times-frac_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	2736
1	764	2443
2	3024	2250

Stop Event

1×	node limit

Counts

123 → 148

prune358.0ms (3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	163	14	177

Error

0.0b

Counts

177 → 14

Alt Table

Status	Error	Program
	8.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 u1) 3/2)) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	1.6b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))) 3) 1/3))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (-.f32 (pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) 3) (pow.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 3)) (+.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (+.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))))
	0.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	12.1b	(.f32 (-.f32 (exp.f32 (log1p.f32 (sqrt.f32 (log1p.f32 u1)))) 1) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 1 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
	8.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))))

Compiler

Compiled 6094 to 3792 computations (37.8% saved)

localize78.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
✓	0.5b	(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
✓	0.5b	(.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))
✓	29.1b	(fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))

series1.8s (15%)

Counts

4 → 44

Calls

4 calls:

1.5s	(fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))
216.0ms	(.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))
6.0ms	(.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
5.0ms	(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)

rewrite47.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

787×	`expm1-log1p-u_binary32`
602×	`prod-diff_binary32`
106×	`add-sqr-sqrt_binary32`
102×	`log1p-expm1-u_binary32`
100×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	76
1	244	54
2	2622	54

Stop Event

1×	node limit

Counts

4 → 84

Calls

4 calls:

46.0ms	(.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
46.0ms	(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
46.0ms	(.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))
46.0ms	(fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

838×	`associate-l_binary32`
549×	`fma-def_binary32`
297×	`cancel-sign-sub-inv_binary32`
242×	`*-commutative_binary32`
169×	`fma-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1337
1	299	1245
2	1045	944
3	4825	938

Stop Event

1×	node limit

Counts

128 → 99

prune1.8s (15.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	456	3	459
Fresh	3	8	11
Picked	1	0	1
Done	0	2	2
Total	460	13	473

Error

0.0b

Counts

473 → 13

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2))) 2) 3))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (-.f32 (pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) 3) (pow.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 3)) (+.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (+.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) 0))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	12.1b	(.f32 (-.f32 (exp.f32 (log1p.f32 (sqrt.f32 (log1p.f32 u1)))) 1) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	8.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 u1) 3/2)) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (log.f32 (pow.f32 (exp.f32 u2) (PI.f32))))))
	8.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))

Compiler

Compiled 43531 to 20140 computations (53.7% saved)

localize88.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)
	0.5b	(.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))
✓	0.7b	(pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2) 3)
	29.1b	(fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))

series177.0ms (1.5%)

Counts

1 → 12

Calls

1 calls:

177.0ms

(pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2) 3)

rewrite38.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`log1p-expm1-u_binary32`
747×	`expm1-log1p-u_binary32`
225×	`prod-diff_binary32`
91×	`add-sqr-sqrt_binary32`
87×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	205	10
2	2178	10

Stop Event

1×	node limit

Counts

1 → 28

Calls

1 calls:

37.0ms

(pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (*.f32 (PI.f32) u2))) 2) 3)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

744×	`cancel-sign-sub-inv_binary32`
543×	`fma-neg_binary32`
458×	`distribute-rgt-neg-in_binary32`
445×	`distribute-lft-neg-in_binary32`
395×	`associate-r_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	356
1	115	352
2	383	282
3	2401	218

Stop Event

1×	node limit

Counts

40 → 38

prune1.3s (11.2%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	346	3	349
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	348	14	362

Error

0.0b

Counts

362 → 14

Alt Table

Status	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2))) 2) 3))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 4)))) 1) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2))) 2) 3))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2))) (cbrt.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (neg.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))) (fma.f32 (neg.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) 1 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 1))))
	8.2b	(.f32 (pow.f32 (pow.f32 (log1p.f32 u1) 1/4) 2) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (/.f32 (-.f32 (pow.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) 3) (pow.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) 3)) (+.f32 (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2)) (+.f32 (.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) u2)) 2) (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))))))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)))))) 0))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (pow.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2))) 2) 3))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 4))))))
	8.2b	(.f32 (.f32 (cbrt.f32 (log1p.f32 u1)) (cbrt.f32 (sqrt.f32 (log1p.f32 u1)))) (cos.f32 (.f32 2 (.f32 (PI.f32) u2))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 2 (-.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) u2))) 1))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (+.f32 (fma.f32 (cos.f32 (.f32 (PI.f32) u2)) (cos.f32 (.f32 (PI.f32) u2)) (neg.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) 2) 6) (pow.f32 (cbrt.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) u2)))) 6)))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2))) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (.f32 (cbrt.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) u2)) 2)) (cbrt.f32 (pow.f32 (sin.f32 (*.f32 (PI.f32) u2)) 2)))))))
	12.1b	(.f32 (-.f32 (exp.f32 (log1p.f32 (sqrt.f32 (log1p.f32 u1)))) 1) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 2))))))
	8.2b	(.f32 (cbrt.f32 (pow.f32 (log1p.f32 u1) 3/2)) (cos.f32 (.f32 2 (*.f32 (PI.f32) u2))))

Compiler

Compiled 28103 to 12772 computations (54.6% saved)

regimes1.9s (16.3%)

Accuracy

Total 0.2b remaining (61.6%)

Threshold costs 0.2b (61.6%)

Counts

143 → 1

Compiler

Compiled 65860 to 41166 computations (37.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	24	25
2	28	25
3	30	25

Stop Event

1×

saturated

end271.0ms (2.3%)

Compiler: Compiled 624 to 407 computations (34.8% saved)

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21

Details

analyze409.0ms (3.5%)

sample2.2s (18.4%)

simplify14.0ms (0.1%)

prune4.0ms (0%)

localize34.0ms (0.3%)

series145.0ms (1.2%)

rewrite52.0ms (0.4%)

simplify44.0ms (0.4%)

prune217.0ms (1.8%)

localize47.0ms (0.4%)

series562.0ms (4.8%)

rewrite54.0ms (0.5%)

simplify58.0ms (0.5%)

prune358.0ms (3%)

localize78.0ms (0.7%)

series1.8s (15%)

rewrite47.0ms (0.4%)

simplify50.0ms (0.4%)

prune1.8s (15.5%)

localize88.0ms (0.7%)

series177.0ms (1.5%)

rewrite38.0ms (0.3%)

simplify26.0ms (0.2%)

prune1.3s (11.2%)

regimes1.9s (16.3%)

simplify2.0ms (0%)

end271.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	14	22
1	26	21
2	39	21
3	49	21
4	60	21
5	74	21
6	92	21
7	119	21
8	149	21
9	162	21
10	184	21
11	206	21
12	245	21
13	262	21
14	268	21
15	269	21