Details

analyze412.0ms (5.1%)

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)

sample2.1s (26.3%)

Results

2.1s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

40×	`fma-neg_binary32`
22×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
15×	`fma-def_binary32`
11×	`*-commutative_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

prune4.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	12.5b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series206.0ms (2.5%)

Counts

4 → 52

Calls

4 calls:

190.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
10.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
3.0ms	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
3.0ms	(.f32 (.f32 2 (PI.f32)) u2)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary32`
18×	`add-sqr-sqrt_binary32`
14×	`associate-l_binary32`
13×	`*-un-lft-identity_binary32`
13×	`add-cube-cbrt_binary32`

Counts

4 → 82

Calls

4 calls:

6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
4.0ms	(.f32 (.f32 2 (PI.f32)) u2)
2.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
1.0ms	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))

simplify114.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

532×	`cancel-sign-sub-inv_binary32`
449×	`fma-neg_binary32`
324×	`times-frac_binary32`
243×	`associate-/r*_binary32`
229×	`associate-/l*_binary32`

Counts

134 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	3614
1	751	3315
2	2419	3199
3	4597	3191
4	5025	3191

prune221.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	157	11	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	158	12	170

Error

0.0b

Counts

170 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.6b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	6.1b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))
	12.5b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	1.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.5b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
	1.8b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 5047 to 3090 computations (38.8% saved)

localize43.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
✓	0.3b	(*.f32 u2 (PI.f32))
✓	1.5b	(exp.f32 (log.f32 (.f32 2 (.f32 u2 (PI.f32)))))

series184.0ms (2.3%)

Counts

3 → 44

Calls

3 calls:

179.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
3.0ms	(exp.f32 (log.f32 (.f32 2 (.f32 u2 (PI.f32)))))
2.0ms	(*.f32 u2 (PI.f32))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary32`
16×	`associate-l_binary32`
13×	`pow1_binary32`
11×	`sqrt-prod_binary32`
11×	`*-un-lft-identity_binary32`

Counts

3 → 68

Calls

3 calls:

6.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
4.0ms	(exp.f32 (log.f32 (.f32 2 (.f32 u2 (PI.f32)))))
3.0ms	(*.f32 u2 (PI.f32))

simplify106.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-neg_binary32`
537×	`fma-def_binary32`
294×	`cancel-sign-sub-inv_binary32`
285×	`associate-+l+_binary32`
189×	`associate--l+_binary32`

Counts

112 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	2569
1	524	2395
2	1579	2292
3	4793	2286
4	5420	2286

prune195.0ms (2.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	159	12	171

Error

0.0b

Counts

171 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.6b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	6.1b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))
	12.5b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	1.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.5b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
	1.8b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 5066 to 3064 computations (39.5% saved)

localize40.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))
✓	0.3b	(.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))
✓	0.4b	(.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2))

series139.0ms (1.7%)

Counts

3 → 24

Calls

3 calls:

123.0ms

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

9.0ms

(*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2))

6.0ms

(*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary32`
19×	`add-exp-log_binary32`
19×	`pow1_binary32`
17×	`sqrt-prod_binary32`
16×	`add-sqr-sqrt_binary32`

Counts

3 → 80

Calls

3 calls:

7.0ms

(*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))

7.0ms

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

5.0ms

(*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2))

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-def_binary32`
468×	`fma-neg_binary32`
304×	`associate-l_binary32`
300×	`cancel-sign-sub-inv_binary32`
228×	`associate-r_binary32`

Counts

104 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	236	2675
1	604	2461
2	1989	2361
3	4662	2357
4	4970	2357

prune219.0ms (2.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	174	12	186

Error

0.0b

Counts

186 → 12

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
▶	0.4b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.6b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	1.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	6.1b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))
	12.5b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	1.5b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.5b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))
	1.8b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 5646 to 3185 computations (43.6% saved)

localize45.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series1.2s (14.6%)

Counts

3 → 52

Calls

3 calls:

693.0ms

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

308.0ms

(*.f32 (cbrt.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))

185.0ms

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

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary32`
24×	`pow1_binary32`
20×	`associate-l_binary32`
19×	`cbrt-prod_binary32`
19×	`add-exp-log_binary32`

Counts

3 → 100

Calls

3 calls:

12.0ms

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

10.0ms

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

6.0ms

(*.f32 (cbrt.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))

simplify153.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

784×	`cancel-sign-sub-inv_binary32`
580×	`times-frac_binary32`
419×	`associate-r_binary32`
331×	`associate-l_binary32`
234×	`*-commutative_binary32`

Counts

152 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	307	6303
1	849	5621
2	3055	5225
3	5221	5225

prune552.0ms (6.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	283	5	288
Fresh	5	4	9
Picked	1	0	1
Done	0	2	2
Total	289	11	300

Error

0.0b

Counts

300 → 11

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) 2))))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (cbrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(.f32 (expm1.f32 (log1p.f32 (.f32 (cbrt.f32 (pow.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32)))) 2)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	0.5b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (.f32 (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (.f32 (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (.f32 (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.5b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.8b	(.f32 (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.3b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	1.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (.f32 (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cbrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cbrt.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (exp.f32 (log.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))

Compiler

Compiled 11842 to 7688 computations (35.1% saved)

regimes1.7s (21.2%)

Accuracy

Total 0.2b remaining (71.3%)

Threshold costs 0.2b (71.3%)

Counts

139 → 1

Compiler

Compiled 43782 to 34866 computations (20.4% saved)

simplify4.0ms (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	16	27
1	27	27
2	32	27
3	34	27
4	33	27

end215.0ms (2.6%)

Compiler: Compiled 424 to 325 computations (23.3% saved)

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21

Details

analyze412.0ms (5.1%)

sample2.1s (26.3%)

simplify14.0ms (0.2%)

prune4.0ms (0.1%)

localize33.0ms (0.4%)

series206.0ms (2.5%)

rewrite16.0ms (0.2%)

simplify114.0ms (1.4%)

prune221.0ms (2.7%)

localize43.0ms (0.5%)

series184.0ms (2.3%)

rewrite16.0ms (0.2%)

simplify106.0ms (1.3%)

prune195.0ms (2.4%)

localize40.0ms (0.5%)

series139.0ms (1.7%)

rewrite29.0ms (0.4%)

simplify99.0ms (1.2%)

prune219.0ms (2.7%)

localize45.0ms (0.6%)

series1.2s (14.6%)

rewrite39.0ms (0.5%)

simplify153.0ms (1.9%)

prune552.0ms (6.8%)

regimes1.7s (21.2%)

simplify4.0ms (0%)

end215.0ms (2.6%)

Profiling

Iter	Nodes	Cost
0	14	22
1	26	21
2	38	21
3	46	21
4	56	21
5	67	21
6	82	21
7	106	21
8	119	21
9	125	21
10	144	21
11	140	21
12	167	21
13	180	21
14	184	21
15	185	21
16	163	21