Details

analyze356.0ms (2.6%)

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 31 to 25 computations (19.4% saved)

sample50.0ms (0.4%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 50 to 42 computations (16% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`sub-neg_binary32`
17×	`cancel-sign-sub-inv_binary32`
11×	`*-commutative_binary32`
9×	`distribute-rgt-neg-in_binary32`
8×	`+-commutative_binary32`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	26	22
2	37	22
3	44	22
4	51	22
5	60	22
6	74	22
7	97	22
8	108	22
9	110	22
10	127	22
11	123	22
12	134	22
13	137	22
14	138	22
15	116	22

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

12.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	12.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
0.1b	(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
0.3b	(.f32 (.f32 2 PI.f32) u2)
12.9b	(log.f32 (-.f32 1 u1))

rewrite167.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

8.0b

Rules

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

Counts

4 → 88

Calls

4 calls:

9.0ms	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
5.0ms	(.f32 (.f32 2 PI.f32) u2)
4.0ms	(log.f32 (-.f32 1 u1))
2.0ms	(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))

Compiler

Compiled 1523 to 1205 computations (20.9% saved)

series110.0ms (0.8%)

Error

0.4b

Counts

4 → 21

Calls

4 calls:

47.0ms	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
14.0ms	(log.f32 (-.f32 1 u1))
13.0ms	(sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))
11.0ms	(.f32 (.f32 2 PI.f32) u2)

Compiler

Compiled 1082 to 905 computations (16.4% saved)

simplify112.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

432×	`sub-neg_binary32`
400×	`cancel-sign-sub-inv_binary32`
391×	`*-commutative_binary32`
264×	`unsub-neg_binary32`
251×	`distribute-rgt-neg-in_binary32`

Counts

109 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	2024
1	414	1890
2	1161	1846
3	2077	1821
4	4151	1821
5	4967	1821

prune130.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	63	12	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Error

0.2b

Counts

76 → 12

Alt Table

Status	Error	Program
	13.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 PI.f32) u2))))
	4.7b	(.f32 (sqrt.f32 (neg.f32 (.f32 u1 (+.f32 -1 (.f32 u1 -1/2))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.3b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
▶	2.4b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log.f32 (-.f32 1 u1))) (cbrt.f32 (log.f32 (-.f32 1 u1))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))))))
	3.2b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	12.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (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))))))
	8.7b	(.f32 (sqrt.f32 (neg.f32 (neg.f32 u1))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.4b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.3b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (sqrt.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	12.3b	(log.f32 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u1 u1))) (log.f32 (+.f32 u1 1))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))

Compiler

Compiled 1686 to 1314 computations (22.1% saved)

localize63.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))
0.3b	(.f32 (.f32 2 PI.f32) u2)
0.4b	(*.f32 u1 1/3)
0.4b	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))

rewrite247.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`pow1_binary32`
16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
15×	`add-sqr-sqrt_binary32`
11×	`*-un-lft-identity_binary32`

Counts

4 → 83

Calls

4 calls:

11.0ms	(sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))
10.0ms	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
5.0ms	(.f32 (.f32 2 PI.f32) u2)
4.0ms	(*.f32 u1 1/3)

Compiler

Compiled 2708 to 1900 computations (29.8% saved)

series91.0ms (0.7%)

Error

0.2b

Counts

4 → 21

Calls

4 calls:

27.0ms	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
20.0ms	(sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4))))
14.0ms	(.f32 (.f32 2 PI.f32) u2)
13.0ms	(*.f32 u1 1/3)

Compiler

Compiled 1019 to 827 computations (18.8% saved)

simplify145.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

286×	`associate-l_binary32`
258×	`sub-neg_binary32`
251×	`distribute-rgt-in_binary32`
236×	`distribute-lft-in_binary32`
231×	`unswap-sqr_binary32`

Counts

104 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	1997
1	449	1804
2	1499	1763
3	3623	1763
4	4540	1763
5	4991	1763
6	4825	1763

prune173.0ms (1.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	71	16	87

Error

0.2b

Counts

87 → 16

Alt Table

Status	Error	Program
	13.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 PI.f32) u2))))
	4.7b	(.f32 (sqrt.f32 (neg.f32 (.f32 u1 (+.f32 -1 (.f32 u1 -1/2))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	2.5b	(.f32 (/.f32 (sqrt.f32 (+.f32 (pow.f32 (+.f32 u1 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2))) 3) (.f32 (pow.f32 u1 12) 1/64))) (sqrt.f32 (+.f32 (.f32 (pow.f32 u1 8) 1/16) (.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 u1 1/3)))) u1) (-.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 u1 1/3)))) u1) (.f32 (pow.f32 u1 4) -1/4)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.6b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	12.3b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.7b	(.f32 (.f32 (.f32 (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log.f32 (-.f32 1 u1))) (cbrt.f32 (log.f32 (-.f32 1 u1))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))))))
	3.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (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))))))
	7.7b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
▶	2.4b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))))))
	8.7b	(.f32 (sqrt.f32 (neg.f32 (neg.f32 u1))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.4b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.3b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (sqrt.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	12.3b	(log.f32 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u1 u1))) (log.f32 (+.f32 u1 1))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))

Compiler

Compiled 2579 to 1935 computations (25% saved)

localize72.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(*.f32 u2 PI.f32)
0.4b	(*.f32 u1 1/3)
0.4b	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
0.4b	(.f32 (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (.f32 2 (*.f32 u2 PI.f32))))

rewrite399.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

140×	`pow1_binary32`
76×	`pow-prod-down_binary32`
60×	`sqrt-pow1_binary32`
20×	`add-sqr-sqrt_binary32`
17×	`pow-prod-up_binary32`

Counts

4 → 127

Calls

4 calls:

12.0ms	(.f32 (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (.f32 2 (*.f32 u2 PI.f32))))
8.0ms	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
4.0ms	(*.f32 u1 1/3)
4.0ms	(*.f32 u2 PI.f32)

Compiler

Compiled 3583 to 2358 computations (34.2% saved)

series96.0ms (0.7%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

27.0ms	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
20.0ms	(.f32 (sqrt.f32 (.f32 2 (.f32 u2 PI.f32))) (sqrt.f32 (.f32 2 (*.f32 u2 PI.f32))))
16.0ms	(*.f32 u1 1/3)
16.0ms	(*.f32 u2 PI.f32)

Compiler

Compiled 1182 to 911 computations (22.9% saved)

simplify126.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

406×	`*-commutative_binary32`
312×	`unswap-sqr_binary32`
275×	`associate-l_binary32`
265×	`exp-prod_binary32`
223×	`distribute-rgt-neg-out_binary32`

Counts

142 → 104

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	166	1513
1	353	1291
2	1190	1253
3	2325	1239
4	4709	1228
5	4995	1228
6	4857	1228

prune214.0ms (1.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	15	15
Picked	1	0	1
Done	0	0	0
Total	103	17	120

Error

0.1b

Counts

120 → 17

Alt Table

Status	Error	Program
	13.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 PI.f32) u2))))
	4.7b	(.f32 (sqrt.f32 (neg.f32 (.f32 u1 (+.f32 -1 (.f32 u1 -1/2))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	2.5b	(.f32 (/.f32 (sqrt.f32 (+.f32 (pow.f32 (+.f32 u1 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2))) 3) (.f32 (pow.f32 u1 12) 1/64))) (sqrt.f32 (+.f32 (.f32 (pow.f32 u1 8) 1/16) (.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 u1 1/3)))) u1) (-.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 u1 1/3)))) u1) (.f32 (pow.f32 u1 4) -1/4)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.6b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.4b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (.f32 (sqrt.f32 2) (sqrt.f32 (.f32 u2 (.f32 PI.f32 2)))) (sqrt.f32 (.f32 u2 PI.f32)))))
	12.3b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.7b	(.f32 (.f32 (.f32 (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log.f32 (-.f32 1 u1))) (cbrt.f32 (log.f32 (-.f32 1 u1))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))))))
	3.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (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))))))
	7.7b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	8.7b	(.f32 (sqrt.f32 (neg.f32 (neg.f32 u1))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.4b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
▶	2.4b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (sqrt.f32 2) (.f32 (sqrt.f32 (.f32 u2 (.f32 PI.f32 2))) (sqrt.f32 (.f32 u2 PI.f32))))))
	13.3b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (sqrt.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	12.3b	(log.f32 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u1 u1))) (log.f32 (+.f32 u1 1))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))

Compiler

Compiled 2759 to 2032 computations (26.4% saved)

localize85.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 u2 (.f32 PI.f32 2))
0.3b	(.f32 (sqrt.f32 (.f32 u2 (.f32 PI.f32 2))) (sqrt.f32 (.f32 u2 PI.f32)))
0.4b	(*.f32 u1 1/3)
0.4b	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))

rewrite304.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

39×	`pow1_binary32`
24×	`pow-prod-down_binary32`
18×	`add-cbrt-cube_binary32`
18×	`add-exp-log_binary32`
15×	`add-sqr-sqrt_binary32`

Counts

4 → 89

Calls

4 calls:

10.0ms	(.f32 (sqrt.f32 (.f32 u2 (.f32 PI.f32 2))) (sqrt.f32 (.f32 u2 PI.f32)))
9.0ms	(.f32 u2 (.f32 PI.f32 2))
8.0ms	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
4.0ms	(*.f32 u1 1/3)

Compiler

Compiled 3163 to 2096 computations (33.7% saved)

series104.0ms (0.8%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

30.0ms	(.f32 (.f32 u1 u1) (-.f32 -1/2 (*.f32 u1 1/3)))
19.0ms	(.f32 (sqrt.f32 (.f32 u2 (.f32 PI.f32 2))) (sqrt.f32 (.f32 u2 PI.f32)))
18.0ms	(.f32 u2 (.f32 PI.f32 2))
16.0ms	(*.f32 u1 1/3)

Compiler

Compiled 1219 to 963 computations (21% saved)

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

490×	`*-commutative_binary32`
445×	`neg-mul-1_binary32`
309×	`associate-l_binary32`
232×	`associate-r_binary32`
223×	`distribute-rgt-neg-out_binary32`

Counts

104 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	170	1516
1	378	1343
2	1264	1343
3	2334	1343
4	4447	1343
5	5038	1343

prune194.0ms (1.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	16	16
Picked	1	0	1
Done	0	0	0
Total	74	17	91

Error

0.1b

Counts

91 → 17

Alt Table

Status	Error	Program
	13.3b	(.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (sqrt.f32 (cos.f32 (.f32 (.f32 2 PI.f32) u2))))
	4.7b	(.f32 (sqrt.f32 (neg.f32 (.f32 u1 (+.f32 -1 (.f32 u1 -1/2))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	2.5b	(.f32 (/.f32 (sqrt.f32 (+.f32 (pow.f32 (+.f32 u1 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2))) 3) (.f32 (pow.f32 u1 12) 1/64))) (sqrt.f32 (+.f32 (.f32 (pow.f32 u1 8) 1/16) (.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 u1 1/3)))) u1) (-.f32 (-.f32 (.f32 u1 (.f32 u1 (-.f32 -1/2 (.f32 u1 1/3)))) u1) (.f32 (pow.f32 u1 4) -1/4)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.6b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4))))) (sqrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.4b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (.f32 (sqrt.f32 2) (sqrt.f32 (.f32 u2 (.f32 PI.f32 2)))) (sqrt.f32 (.f32 u2 PI.f32)))))
	12.3b	(.f32 (.f32 (fabs.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.7b	(.f32 (.f32 (.f32 (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cbrt.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (log.f32 (-.f32 1 u1))) (cbrt.f32 (log.f32 (-.f32 1 u1))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (sqrt.f32 (neg.f32 (cbrt.f32 (log.f32 (-.f32 1 u1)))))))
	3.1b	(.f32 (exp.f32 (log.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.3b	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (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))))))
	7.7b	(.f32 (log.f32 (exp.f32 (sqrt.f32 (+.f32 (.f32 (.f32 u1 u1) (+.f32 (.f32 u1 1/3) 1/2)) (+.f32 u1 (.f32 (pow.f32 u1 4) 1/4)))))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	8.7b	(.f32 (sqrt.f32 (neg.f32 (neg.f32 u1))) (cos.f32 (.f32 (*.f32 2 PI.f32) u2)))
	12.4b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))) (.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))) (cbrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))))))
	13.3b	(.f32 (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (sqrt.f32 (cos.f32 (.f32 2 (.f32 u2 PI.f32))))) (.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (sqrt.f32 (cos.f32 (.f32 2 (*.f32 u2 PI.f32))))))
	12.3b	(log.f32 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1))))) (cos.f32 (.f32 2 (.f32 u2 PI.f32)))))
	13.3b	(.f32 (sqrt.f32 (neg.f32 (-.f32 (log.f32 (-.f32 1 (.f32 u1 u1))) (log.f32 (+.f32 u1 1))))) (cos.f32 (.f32 (.f32 2 PI.f32) u2)))
	2.4b	(.f32 (sqrt.f32 (neg.f32 (+.f32 (-.f32 (.f32 (.f32 u1 u1) (-.f32 -1/2 (.f32 u1 1/3))) u1) (.f32 (pow.f32 u1 4) -1/4)))) (cos.f32 (.f32 (sqrt.f32 2) (sqrt.f32 (.f32 2 (.f32 (pow.f32 PI.f32 2) (*.f32 u2 u2)))))))

Compiler

Compiled 2437 to 1686 computations (30.8% saved)

regimes7.7s (55.9%)

Accuracy

Total 0.3b remaining (61.9%)

Threshold costs 0.3b (61.9%)

Compiler

Compiled 86130 to 68734 computations (20.2% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`distribute-rgt-neg-in_binary32`
27×	`cancel-sign-sub-inv_binary32`
21×	`*-commutative_binary32`
20×	`distribute-lft-neg-in_binary32`
20×	`neg-sub0_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	107
1	71	107
2	102	105
3	129	105
4	161	105
5	184	105
6	204	105
7	220	105
8	224	105
9	215	105

end8.0ms (0.1%)

Compiler: Compiled 67 to 55 computations (17.9% saved)

sample2.7s (19.3%)

Algorithm

1×

intervals

Results

733.0ms	8000×	body	128	valid
238.0ms	8000×	pre	128	true
0.0ms	6×	pre	128	false

Compiler

Compiled 672 to 541 computations (19.5% saved)

Iter	Nodes	Cost
0	14	22
1	26	22
2	37	22
3	44	22
4	51	22
5	60	22
6	74	22
7	97	22
8	108	22
9	110	22
10	127	22
11	123	22
12	134	22
13	137	22
14	138	22
15	116	22

Iter	Nodes	Cost
0	42	107
1	71	107
2	102	105
3	129	105
4	161	105
5	184	105
6	204	105
7	220	105
8	224	105
9	215	105

Iter	Nodes	Cost
0	14	22
1	26	22
2	37	22
3	44	22
4	51	22
5	60	22
6	74	22
7	97	22
8	108	22
9	110	22
10	127	22
11	123	22
12	134	22
13	137	22
14	138	22
15	116	22

Iter	Nodes	Cost
0	42	107
1	71	107
2	102	105
3	129	105
4	161	105
5	184	105
6	204	105
7	220	105
8	224	105
9	215	105

Details

analyze356.0ms (2.6%)

sample50.0ms (0.4%)

simplify15.0ms (0.1%)

prune6.0ms (0%)

localize33.0ms (0.2%)

rewrite167.0ms (1.2%)

series110.0ms (0.8%)

simplify112.0ms (0.8%)

prune130.0ms (0.9%)

localize63.0ms (0.5%)

rewrite247.0ms (1.8%)

series91.0ms (0.7%)

simplify145.0ms (1.1%)

prune173.0ms (1.3%)

localize72.0ms (0.5%)

rewrite399.0ms (2.9%)

series96.0ms (0.7%)

simplify126.0ms (0.9%)

prune214.0ms (1.6%)

localize85.0ms (0.6%)

rewrite304.0ms (2.2%)

series104.0ms (0.8%)

simplify104.0ms (0.8%)

prune194.0ms (1.4%)

regimes7.7s (55.9%)

bsearch10.0ms (0.1%)

simplify11.0ms (0.1%)

end8.0ms (0.1%)

sample2.7s (19.3%)

Profiling

Iter	Nodes	Cost
0	14	22
1	26	22
2	37	22
3	44	22
4	51	22
5	60	22
6	74	22
7	97	22
8	108	22
9	110	22
10	127	22
11	123	22
12	134	22
13	137	22
14	138	22
15	116	22

Iter	Nodes	Cost
0	42	107
1	71	107
2	102	105
3	129	105
4	161	105
5	184	105
6	204	105
7	220	105
8	224	105
9	215	105