Details

analyze1.9s (12.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample211.0ms (1.4%)

Algorithm

1×

intervals

Results

159.0ms	157×	body	1024	valid
29.0ms	46×	body	512	valid
7.0ms	42×	body	128	valid
4.0ms	11×	body	256	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify106.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

645×	`associate-/r*_binary64`
634×	`sqr-pow_binary64`
437×	`cube-prod_binary64`
394×	`associate-l_binary64`
368×	`*-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	26	26
2	36	26
3	64	26
4	133	26
5	336	26
6	1035	26
7	1732	26
8	2420	26
9	2633	26
10	2904	26
11	3259	26
12	3653	26
13	4555	26
14	4873	26
15	4875	26

prune2.0ms (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

4.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	4.5b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))

Compiler

Compiled 38 to 28 computations (26.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite172.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

4.3b

Rules

46×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
24×	`times-frac_binary64`

Counts

4 → 102

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.0ms	(pow.f64 (sin.f64 kx) 2)
2.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2341 to 1310 computations (44% saved)

series115.0ms (0.8%)

Error

2.0b

Counts

4 → 28

Calls

4 calls:

47.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
39.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(pow.f64 (sin.f64 kx) 2)
8.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1448 to 1010 computations (30.2% saved)

simplify149.0ms (1%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary64`
381×	`associate-/l*_binary64`
333×	`associate-r_binary64`
306×	`associate-/r*_binary64`
297×	`associate-l_binary64`

Counts

130 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2705
1	390	2600
2	1093	2564
3	4768	2564
4	4973	2564
5	4947	2564

prune65.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	12	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	12	75

Error

1.9b

Counts

75 → 12

Alt Table

Status	Error	Program
	14.4b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) 3)) (sin.f64 th))
	11.7b	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) (sin.f64 th))
▶	4.5b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
	6.7b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 6)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
	5.1b	(.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 ky) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	5.6b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	5.6b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	5.2b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	5.0b	(.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
	47.1b	(.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
	46.9b	(.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
	11.7b	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6)))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 kx) 2)) (-.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 ky) 2)) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))

Compiler

Compiled 1781 to 1083 computations (39.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite162.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

46×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
24×	`times-frac_binary64`

Counts

4 → 102

Calls

4 calls:

11.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.0ms	(pow.f64 (sin.f64 kx) 2)
2.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2519 to 1488 computations (40.9% saved)

series119.0ms (0.8%)

Error

1.9b

Counts

4 → 28

Calls

4 calls:

50.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
34.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(pow.f64 (sin.f64 ky) 2)
9.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1574 to 1136 computations (27.8% saved)

simplify145.0ms (1%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary64`
381×	`associate-/l*_binary64`
333×	`associate-r_binary64`
306×	`associate-/r*_binary64`
297×	`associate-l_binary64`

Counts

130 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2705
1	390	2600
2	1093	2564
3	4768	2564
4	4973	2564
5	4947	2564

prune80.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	75	11	86

Error

1.9b

Counts

86 → 11

Alt Table

Status	Error	Program
	5.6b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
▶	4.9b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
	5.1b	(.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 ky) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	5.6b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	5.2b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	14.4b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) 3)) (sin.f64 th))
	5.0b	(.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
	47.1b	(.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
	46.9b	(.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
	11.7b	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6)))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 kx) 2)) (-.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 ky) 2)) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
✓	4.5b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))

Compiler

Compiled 1782 to 1109 computations (37.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 kx))
0.6b	(cbrt.f64 (sin.f64 kx))
0.7b	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.3b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite96.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(cbrt.f64 (sin.f64 kx))
3.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
1.0ms	(cbrt.f64 (sin.f64 kx))

Compiler

Compiled 1847 to 975 computations (47.2% saved)

series121.0ms (0.8%)

Error

1.9b

Counts

4 → 28

Calls

4 calls:

36.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
25.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
18.0ms	(cbrt.f64 (sin.f64 kx))
18.0ms	(cbrt.f64 (sin.f64 kx))

Compiler

Compiled 1975 to 1438 computations (27.2% saved)

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

492×	`associate-l_binary64`
479×	`times-frac_binary64`
398×	`associate-r_binary64`
279×	`associate-/r*_binary64`
208×	`cancel-sign-sub-inv_binary64`

Counts

86 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	1488
1	373	1195
2	942	1151
3	3822	1148
4	4649	1148
5	4887	1148

prune74.0ms (0.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	60	11	71

Error

1.9b

Counts

71 → 11

Alt Table

Status	Error	Program
	5.2b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 kx))) 8) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 kx))) 4)) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
✓	4.5b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
	5.1b	(.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 ky) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	5.6b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
✓	4.9b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
	14.4b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) 3)) (sin.f64 th))
▶	5.0b	(.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
	5.5b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) (sin.f64 th))
	47.1b	(.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
	46.9b	(.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
	11.7b	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6)))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 kx) 2)) (-.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 ky) 2)) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))

Compiler

Compiled 1988 to 1241 computations (37.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.4b	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.6b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite267.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

78×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`
45×	`sqrt-prod_binary64`
36×	`add-cube-cbrt_binary64`

Counts

4 → 138

Calls

4 calls:

16.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
9.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
8.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3498 to 2203 computations (37% saved)

series151.0ms (1%)

Error

1.9b

Counts

4 → 30

Calls

4 calls:

48.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
40.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
35.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1536 to 1106 computations (28% saved)

simplify165.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

407×	`associate-l_binary64`
380×	`associate-r_binary64`
364×	`distribute-neg-frac_binary64`
313×	`times-frac_binary64`
266×	`div-sub_binary64`

Counts

168 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	3584
1	364	3412
2	976	3385
3	3680	3385
4	4546	3385
5	4937	3385

prune82.0ms (0.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	6	8
Picked	0	1	1
Done	2	0	2
Total	108	10	118

Error

1.9b

Counts

118 → 10

Alt Table

Status	Error	Program
	28.2b	(*.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 ky))) (sin.f64 th))
	5.5b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) (sin.f64 th))
	5.5b	(.f64 (.f64 (sin.f64 ky) (*.f64 (fabs.f64 (cbrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sqrt.f64 (cbrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) (sin.f64 th))
	11.7b	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6)))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 kx) 2)) (-.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 ky) 2)) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
	8.3b	(.f64 (.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) 3))) (sin.f64 th))
	14.4b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) 3)) (sin.f64 th))
	5.0b	(.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
	47.1b	(.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx))))) (sin.f64 th))
	46.9b	(.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky))))) (sin.f64 th))
	5.2b	(.f64 (.f64 1 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 kx))) 8) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 kx))) 4)) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))

Compiler

Compiled 1703 to 1045 computations (38.6% saved)

regimes3.2s (21.2%)

Accuracy

Total 1.5b remaining (44%)

Threshold costs 0b (0%)

Compiler

Compiled 61048 to 44102 computations (27.8% saved)

bsearch12.0ms (0.1%)

Compiler: Compiled 16 to 12 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	79
1	36	79
2	35	79

end1.0ms (0%)

Compiler: Compiled 52 to 31 computations (40.4% saved)

sample7.5s (49.9%)

Algorithm

1×

intervals

Results

5.5s	4667×	body	1024	valid
890.0ms	1418×	body	512	valid
234.0ms	1389×	body	128	valid
230.0ms	514×	body	256	valid
24.0ms	12×	body	2048	valid

Compiler

Compiled 373 to 261 computations (30% saved)

Details

analyze1.9s (12.4%)

sample211.0ms (1.4%)

simplify106.0ms (0.7%)

prune2.0ms (0%)

localize12.0ms (0.1%)

rewrite172.0ms (1.1%)

series115.0ms (0.8%)

simplify149.0ms (1%)

prune65.0ms (0.4%)

localize17.0ms (0.1%)

rewrite162.0ms (1.1%)

series119.0ms (0.8%)

simplify145.0ms (1%)

prune80.0ms (0.5%)

localize21.0ms (0.1%)

rewrite96.0ms (0.6%)

series121.0ms (0.8%)

simplify104.0ms (0.7%)

prune74.0ms (0.5%)

localize14.0ms (0.1%)

rewrite267.0ms (1.8%)

series151.0ms (1%)

simplify165.0ms (1.1%)

prune82.0ms (0.5%)

regimes3.2s (21.2%)

bsearch12.0ms (0.1%)

simplify4.0ms (0%)

end1.0ms (0%)

sample7.5s (49.9%)

Profiling