Details

analyze376.0ms (4.3%)

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)

sample96.0ms (1.1%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify16.0ms (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

prune5.0ms (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
	14.2b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 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 2 (PI.f32)) u2)))

Compiler

Compiled 90 to 77 computations (14.4% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series200.0ms (2.3%)

Counts

4 → 52

Calls

4 calls:

180.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
11.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
5.0ms	(.f32 (.f32 2 (PI.f32)) u2)
3.0ms	(cos.f32 (.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	(cos.f32 (.f32 (.f32 2 (PI.f32)) u2))
2.0ms	(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))

simplify116.0ms (1.3%)

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

prune227.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	157	11	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

0.1b

Counts

170 → 11

Alt Table

Status	Error	Program
	0.7b	(.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)))
▶	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
	0.5b	(.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)))))
	2.3b	(fma.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 2/3 (.f32 (pow.f32 u2 4) (pow.f32 (PI.f32) 4)) 1) (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (fma.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 u2 6) -4/45) (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 u2 u2) -2)))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	2.0b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	6.8b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.6b	(.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))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))

Compiler

Compiled 5081 to 3094 computations (39.1% saved)

localize58.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
✓	0.3b	(.f32 (.f32 u2 u2) u2)
✓	0.3b	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2))
✓	1.0b	(.f32 (.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))

series201.0ms (2.3%)

Counts

4 → 44

Calls

4 calls:

184.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
13.0ms	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2))
3.0ms	(.f32 (.f32 u2 u2) u2)
0.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))

rewrite119.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

817×	`pow1_binary32`
401×	`pow-prod-down_binary32`
218×	`add-cbrt-cube_binary32`
215×	`add-exp-log_binary32`
213×	`pow-prod-up_binary32`

Counts

4 → 312

Calls

4 calls:

37.0ms	(.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (.f32 u2 u2) u2))
9.0ms	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
5.0ms	(.f32 (.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))
4.0ms	(.f32 (.f32 u2 u2) u2)

simplify213.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-def_binary32`
492×	`associate-l_binary32`
418×	`associate-r_binary32`
284×	`cancel-sign-sub-inv_binary32`
247×	`log-prod_binary32`

Counts

356 → 226

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	7581
1	691	5325
2	2706	5270
3	4246	5256
4	4905	5256
5	4940	5256

prune436.0ms (5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	225	12	237

Error

0.1b

Counts

237 → 12

Alt Table

Status	Error	Program
	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (exp.f32 (log.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.5b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2))))))
	0.7b	(.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)))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
	2.0b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
▶	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	6.8b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.6b	(.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))))
	0.5b	(.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)))))

Compiler

Compiled 8611 to 4829 computations (43.9% saved)

localize41.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
✓	0.2b	(log1p.f32 (.f32 (.f32 2 (PI.f32)) u2))
✓	0.3b	(expm1.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)

series185.0ms (2.1%)

Counts

3 → 44

Calls

3 calls:

175.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))

6.0ms

(log1p.f32 (*.f32 (*.f32 2 (PI.f32)) u2))

4.0ms

(expm1.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`associate-l_binary32`
12×	`add-sqr-sqrt_binary32`
11×	`sqrt-prod_binary32`
8×	`*-un-lft-identity_binary32`
8×	`add-cube-cbrt_binary32`

Counts

3 → 55

Calls

3 calls:

7.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))

0.0ms

(expm1.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))

0.0ms

(log1p.f32 (*.f32 (*.f32 2 (PI.f32)) u2))

simplify104.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

741×	`fma-def_binary32`
500×	`times-frac_binary32`
437×	`fma-neg_binary32`
401×	`cancel-sign-sub-inv_binary32`
286×	`associate-/r*_binary32`

Counts

99 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	2959
1	644	2759
2	2045	2648
3	4634	2628
4	5339	2628

prune247.0ms (2.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	167	12	179

Error

0.1b

Counts

179 → 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)))))
	0.5b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2))))))
	0.7b	(.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)))
✓	0.3b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2)))))
▶	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	2.0b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	6.8b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.6b	(.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))))
	0.7b	(+.f32 (.f32 (.f32 (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cos.f32 1)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sin.f32 1)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
	0.5b	(.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)))))

Compiler

Compiled 5012 to 3032 computations (39.5% saved)

localize54.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))
✓	0.3b	(.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))
	0.4b	(.f32 (.f32 2 (PI.f32)) u2)
✓	0.5b	(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

series42.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

21.0ms

(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

13.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

7.0ms

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

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`pow1_binary32`
61×	`sqrt-prod_binary32`
50×	`add-sqr-sqrt_binary32`
32×	`pow-prod-up_binary32`
31×	`*-un-lft-identity_binary32`

Counts

3 → 163

Calls

3 calls:

16.0ms

(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

8.0ms

(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))

5.0ms

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

simplify112.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary32`
321×	`fma-neg_binary32`
218×	`associate-l_binary32`
209×	`associate-r_binary32`
166×	`times-frac_binary32`

Counts

191 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	3349
1	602	2791
2	1902	2650
3	4660	2650
4	4986	2650

prune633.0ms (7.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	323	3	326
Fresh	2	7	9
Picked	0	1	1
Done	1	1	2
Total	326	12	338

Error

0.1b

Counts

338 → 12

Alt Table

Status	Error	Program
✓	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 u2 (PI.f32)))) (cbrt.f32 (.f32 2 (.f32 u2 (PI.f32))))) (cbrt.f32 (.f32 2 (*.f32 u2 (PI.f32)))))))))
	2.0b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))))
	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))))
	0.8b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	0.5b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (.f32 (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 8 (.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (cos.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (*.f32 u2 u2) u2))))))
✓	0.4b	(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (expm1.f32 (log1p.f32 (.f32 (*.f32 2 (PI.f32)) u2)))))
	6.8b	(log.f32 (pow.f32 (exp.f32 (cos.f32 (.f32 2 (.f32 u2 (PI.f32))))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
	0.9b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 2 (PI.f32)) u2))))
	0.6b	(.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))))
	0.4b	(cbrt.f32 (.f32 (.f32 (cbrt.f32 (pow.f32 (neg.f32 (log1p.f32 (neg.f32 u1))) 3)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2))) (cos.f32 (.f32 (.f32 2 (PI.f32)) u2)))))
	0.7b	(+.f32 (.f32 (.f32 (cos.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (cos.f32 1)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (.f32 (.f32 (sin.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) u2)))) (sin.f32 1)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))

Compiler

Compiled 14793 to 7301 computations (50.6% saved)

regimes3.0s (34.6%)

Accuracy

Total 0.2b remaining (73.5%)

Threshold costs 0.2b (73.5%)

Counts

208 → 1

Compiler

Compiled 62040 to 48394 computations (22% saved)

simplify3.0ms (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	19	34
1	28	34
2	32	34
3	34	34
4	34	34

end1.0ms (0%)

Compiler: Compiled 23 to 21 computations (8.7% saved)

sample2.1s (23.9%)

Algorithm

1×

intervals

Results

931.0ms	8000×	body	128	valid
290.0ms	8000×	pre	128	true
0.0ms	2×	pre	128	false

Compiler

Compiled 473 to 344 computations (27.3% 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

analyze376.0ms (4.3%)

sample96.0ms (1.1%)

simplify16.0ms (0.2%)

prune5.0ms (0.1%)

localize34.0ms (0.4%)

series200.0ms (2.3%)

rewrite16.0ms (0.2%)

simplify116.0ms (1.3%)

prune227.0ms (2.6%)

localize58.0ms (0.7%)

series201.0ms (2.3%)

rewrite119.0ms (1.4%)

simplify213.0ms (2.5%)

prune436.0ms (5%)

localize41.0ms (0.5%)

series185.0ms (2.1%)

rewrite11.0ms (0.1%)

simplify104.0ms (1.2%)

prune247.0ms (2.9%)

localize54.0ms (0.6%)

series42.0ms (0.5%)

rewrite45.0ms (0.5%)

simplify112.0ms (1.3%)

prune633.0ms (7.3%)

regimes3.0s (34.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.1s (23.9%)

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