Details

analyze1.9s (15.6%)

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
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 25 to 23 computations (8% saved)

sample91.0ms (0.7%)

Algorithm

1×

intervals

Results

44.0ms	66×	body	1024	valid
18.0ms	145×	body	128	valid
15.0ms	34×	body	512	valid
3.0ms	11×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify247.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 15.9b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_786`
20×	`pow1_binary64_809`
18×	`add-cbrt-cube_binary64_784`
15×	`*-un-lft-identity_binary64_751`
12×	`prod-exp_binary64_797` `add-sqr-sqrt_binary64_772`
11×	`add-cube-cbrt_binary64_783`
10×	`associate-r_binary64_693`
9×	`pow-prod-down_binary64_819` `cbrt-unprod_binary64_781`
8×	`sqrt-prod_binary64_766`
7×	`unpow-prod-down_binary64_827`
4×	`pow-exp_binary64_816` `add-log-exp_binary64_787` `sqrt-div_binary64_767`
3×	`times-frac_binary64_757` `pow-unpow_binary64_825` `div-exp_binary64_799`
2×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `-commutative_binary64_684` `associate-r/_binary64_695` `associate-l_binary64_694` `flip-+_binary64_725`
1×	`pow-to-exp_binary64_817` `unpow2_binary64_813` `sqr-pow_binary64_723` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `pow-pow_binary64_820` `div-inv_binary64_748` `sqrt-pow1_binary64_768`

Counts

4 → 86

Calls

4 calls:

17.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

series868.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
268.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
218.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
67.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5201	2385

prune197.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	10	99

Merged error: 11.0b

Counts

99 → 10

Compiler

Compiled 3189 to 2572 computations (19.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.2b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
7.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_786`
23×	`pow1_binary64_809`
21×	`add-cbrt-cube_binary64_784`
14×	`prod-exp_binary64_797`
11×	`pow-prod-down_binary64_819` `*-un-lft-identity_binary64_751` `cbrt-unprod_binary64_781`
10×	`add-sqr-sqrt_binary64_772`
9×	`add-cube-cbrt_binary64_783`
7×	`unpow-prod-down_binary64_827`
4×	`pow-exp_binary64_816` `add-log-exp_binary64_787` `sqrt-div_binary64_767` `associate-r/_binary64_695` `sqrt-prod_binary64_766` `associate-r*_binary64_693`
3×	`times-frac_binary64_757` `pow-unpow_binary64_825` `div-exp_binary64_799`
2×	`flip3-+_binary64_754` `-commutative_binary64_684` `associate-l*_binary64_694` `flip-+_binary64_725`
1×	`pow-to-exp_binary64_817` `distribute-lft-out_binary64_704` `unpow2_binary64_813` `sqr-pow_binary64_723` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `pow-pow_binary64_820` `div-inv_binary64_748` `sqrt-pow1_binary64_768`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))

series852.0ms (7%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
277.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
199.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
62.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4984	2306
1	4984	2306

prune167.0ms (1.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 11.0b

Counts

105 → 11

Compiler

Compiled 3044 to 2453 computations (19.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite54.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64_766`
18×	`*-un-lft-identity_binary64_751`
16×	`add-sqr-sqrt_binary64_772`
12×	`sqrt-div_binary64_767`
10×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `sqrt-pow1_binary64_768`
6×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828`
4×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `flip-+_binary64_725`

Counts

4 → 76

Calls

4 calls:

13.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
11.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.5s (12.3%)

Counts

4 → 12

Calls

4 calls:

499.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
497.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
257.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
252.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4952	2368
1	4952	2368

prune257.0ms (2.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	88	11	99

Merged error: 11.0b

Counts

99 → 11

Compiler

Compiled 4570 to 3745 computations (18.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.1b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
14.1b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.1b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_751`
14×	`pow1_binary64_809`
13×	`cbrt-prod_binary64_779` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
11×	`add-sqr-sqrt_binary64_772`
9×	`add-cube-cbrt_binary64_783`
7×	`sqrt-prod_binary64_766`
6×	`prod-exp_binary64_797` `pow-prod-down_binary64_819` `cbrt-unprod_binary64_781` `cbrt-div_binary64_780`
4×	`add-log-exp_binary64_787`
3×	`pow1/3_binary64_830` `distribute-lft-out_binary64_704` `flip3-+_binary64_754` `associate-l_binary64_694` `flip-+_binary64_725`
2×	`rem-sqrt-square_binary64_764` `sqrt-div_binary64_767` `sqrt-pow1_binary64_768`
1×	`pow1/2_binary64_828` `-commutative_binary64_684` `associate-r*_binary64_693`

Counts

4 → 70

Calls

4 calls:

10.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))

series1.8s (14.7%)

Counts

4 → 12

Calls

4 calls:

510.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
503.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
490.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
300.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4889	2721
1	4889	2721

prune235.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	7	7
Picked	1	0	1
Done	1	2	3
Total	83	10	93

Merged error: 11.0b

Counts

93 → 10

Compiler

Compiled 4104 to 3325 computations (19% saved)

regimes161.0ms (1.3%)

Compiler: Compiled 1660 to 1505 computations (9.3% saved)

bsearch144.0ms (1.2%)

Steps

Iters	Range		Point
9	-1.1158641727774906e-274	-1.6068648047531948e-280	-6.654653175289267e-275
9	-2.381193434927242e-149	-6.994665968139149e-155	-1.604721337117701e-154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	80
1	48	80

end0.0ms (0%)

sample3.2s (26.4%)

Algorithm

1×

intervals

Results

1.4s	2052×	body	1024	valid
572.0ms	4427×	body	128	valid
457.0ms	995×	body	512	valid
161.0ms	526×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 405 to 362 computations (10.6% saved)

Details

analyze1.9s (15.6%)

sample91.0ms (0.7%)

simplify247.0ms (2%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite52.0ms (0.4%)

series868.0ms (7.1%)

simplify55.0ms (0.4%)

prune197.0ms (1.6%)

localize16.0ms (0.1%)

rewrite48.0ms (0.4%)

series852.0ms (7%)

simplify73.0ms (0.6%)

prune167.0ms (1.4%)

localize19.0ms (0.2%)

rewrite54.0ms (0.4%)

series1.5s (12.3%)

simplify65.0ms (0.5%)

prune257.0ms (2.1%)

localize22.0ms (0.2%)

rewrite45.0ms (0.4%)

series1.8s (14.7%)

simplify105.0ms (0.9%)

prune235.0ms (1.9%)

regimes161.0ms (1.3%)

bsearch144.0ms (1.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (26.4%)

Profiling