Details

analyze4.4s (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample348.0ms (0.1%)

Algorithm

1×

intervals

Results

78.0ms	19×	body	1024	invalid
75.0ms	204×	body	128	valid
29.0ms	81×	body	128	invalid
26.0ms	19×	body	1024	valid
19.0ms	22×	body	512	valid
12.0ms	13×	body	512	invalid
8.0ms	11×	body	256	valid
5.0ms	2×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify445.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (224.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune7.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 38.5b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.8b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.5b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite163.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_1385`
102×	`flip3--_binary64_1446` `flip--_binary64_1417`
68×	`frac-times_binary64_1452`
66×	`sqrt-div_binary64_1459`
64×	`frac-add_binary64_1450`
44×	`pow1_binary64_1503`
34×	`associate-*r/_binary64_1384`
17×	`pow-prod-down_binary64_1513`
16×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
8×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
6×	`add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`pow-sqr_binary64_1415` `add-log-exp_binary64_1481` `pow-prod-up_binary64_1512`
3×	`sqrt-prod_binary64_1458`
2×	`pow-plus_binary64_1505`
1×	`pow2_binary64_1523` `sqrt-pow1_binary64_1460` `associate-r_binary64_1382` `rem-sqrt-square_binary64_1455` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

4 → 135

Calls

4 calls:

42.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
29.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
11.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.4s (0.8%)

Counts

4 → 12

Calls

4 calls:

1.9s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
381.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
67.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify183.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5228	10334

prune2.2s (0.7%)

Pruning

49 alts after pruning (48 fresh and 1 done)

	Pruned	Kept	Total
New	99	48	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	49	148

Merged error: 24.1b

Counts

148 → 49

Compiler

Compiled 11506 to 4373 computations (62% saved)

localize51.0ms (0%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2))))
2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
35.5b	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite95.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`flip3--_binary64_1446` `flip--_binary64_1417`
18×	`sqrt-div_binary64_1459`
16×	`frac-add_binary64_1450`
8×	`frac-times_binary64_1452`
6×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464`
5×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`associate-r/_binary64_1384` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `associate-l/_binary64_1385`
3×	`sqrt-prod_binary64_1458`
2×	`associate--l+_binary64_1379`
1×	`sqrt-pow1_binary64_1460` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `diff-log_binary64_1534` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

4 → 59

Calls

4 calls:

34.0ms	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
23.0ms	(-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2))))
5.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
5.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series4.4s (1.4%)

Counts

4 → 12

Calls

4 calls:

3.0s	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
1.3s	(-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2))))
35.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
29.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

simplify365.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	5582	5015

prune5.0s (1.6%)

Pruning

82 alts after pruning (80 fresh and 2 done)

	Pruned	Kept	Total
New	37	34	71
Fresh	1	46	47
Picked	0	1	1
Done	0	1	1
Total	38	82	120

Merged error: 17.2b

Counts

120 → 82

Compiler

Compiled 10037 to 5022 computations (50% saved)

localize56.0ms (0%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 3)) 2))))
2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
35.5b	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 3)) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite105.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`flip3--_binary64_1446` `flip--_binary64_1417`
18×	`sqrt-div_binary64_1459`
16×	`frac-add_binary64_1450`
8×	`frac-times_binary64_1452`
6×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464`
5×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`associate-r/_binary64_1384` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `associate-l/_binary64_1385`
3×	`sqrt-prod_binary64_1458`
2×	`associate--l+_binary64_1379`
1×	`sqrt-pow1_binary64_1460` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `diff-log_binary64_1534` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

4 → 59

Calls

4 calls:

40.0ms	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 3)) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
23.0ms	(-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 3)) 2))))
5.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
5.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series5.6s (1.8%)

Counts

4 → 12

Calls

4 calls:

3.8s	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 3)) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
1.7s	(-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 3)) 2))))
72.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
67.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

simplify157.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5591	5015

prune3.1s (1%)

Pruning

86 alts after pruning (83 fresh and 3 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	3	76	79
Picked	0	1	1
Done	0	2	2
Total	67	86	153

Merged error: 17.2b

Counts

153 → 86

Compiler

Compiled 10295 to 5246 computations (49% saved)

localize112.0ms (0%)

Local error

Found 4 expressions with local error:

2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
2.8b	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
35.5b	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2))) (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))) (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite158.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`flip3--_binary64_1446` `flip--_binary64_1417`
18×	`sqrt-div_binary64_1459`
16×	`frac-add_binary64_1450`
8×	`frac-times_binary64_1452`
6×	`add-sqr-sqrt_binary64_1464`
5×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`associate-r/_binary64_1384` `add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `associate-l/_binary64_1385`
3×	`sqrt-prod_binary64_1458`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

4 → 52

Calls

4 calls:

45.0ms	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2))) (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))) (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
13.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
10.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

series3.8s (1.2%)

Counts

4 → 12

Calls

4 calls:

3.7s	(sqrt.f64 (+.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)) 2) (+.f64 (.f64 lambda1 lambda1) (.f64 lambda2 lambda2))) (.f64 2 (.f64 (.f64 lambda1 lambda2) (pow.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2))) (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))) (cbrt.f64 (cos.f64 (.f64 (+.f64 phi1 phi2) 1/2)))) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
66.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
42.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))
31.0ms	(cos.f64 (*.f64 (+.f64 phi1 phi2) 1/2))

simplify265.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5139	4567

prune3.7s (1.2%)

Pruning

101 alts after pruning (97 fresh and 4 done)

	Pruned	Kept	Total
New	45	19	64
Fresh	4	78	82
Picked	0	1	1
Done	0	3	3
Total	49	101	150

Merged error: 17.2b

Counts

150 → 101

Compiler

Compiled 5045 to 2235 computations (55.7% saved)

regimes25.4s (8.2%)

Compiler: Compiled 108336 to 66394 computations (38.7% saved)

bsearch3.6min (69.4%)

Compiler: Compiled 29 to 19 computations (34.5% saved)

simplify47.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	132	148
1	132	148

end0.0ms (0%)

sample31.9s (10.3%)

Algorithm

1×

intervals

Results

1.7s	6080×	body	128	valid
935.0ms	758×	body	1024	valid
703.0ms	2419×	body	128	invalid
644.0ms	510×	body	1024	invalid
576.0ms	755×	body	512	valid
394.0ms	365×	body	512	invalid
207.0ms	400×	body	256	valid
99.0ms	171×	body	256	invalid
9.0ms	7×	body	2048	valid

Compiler

Compiled 12776 to 7822 computations (38.8% saved)

Pareto

0.9443494164111796

Details

analyze4.4s (1.4%)

sample348.0ms (0.1%)

simplify445.0ms (0.1%)

prune7.0ms (0%)

localize38.0ms (0%)

rewrite163.0ms (0.1%)

series2.4s (0.8%)

simplify183.0ms (0.1%)

prune2.2s (0.7%)

localize51.0ms (0%)

rewrite95.0ms (0%)

series4.4s (1.4%)

simplify365.0ms (0.1%)

prune5.0s (1.6%)

localize56.0ms (0%)

rewrite105.0ms (0%)

series5.6s (1.8%)

simplify157.0ms (0.1%)

prune3.1s (1%)

localize112.0ms (0%)

rewrite158.0ms (0.1%)

series3.8s (1.2%)

simplify265.0ms (0.1%)

prune3.7s (1.2%)

regimes25.4s (8.2%)

bsearch3.6min (69.4%)

simplify47.0ms (0%)

end0.0ms (0%)

sample31.9s (10.3%)

Profiling