Details

analyze1.8s (13.8%)

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)

sample101.0ms (0.8%)

Algorithm

1×

intervals

Results

45.0ms	52×	body	1280	valid
21.0ms	40×	body	640	valid
16.0ms	141×	body	80	valid
6.0ms	15×	body	320	valid
2.0ms	8×	body	160	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify189.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (172.0ms)

Iter	Nodes	Cost
0	4872	37
1	4872	37

prune4.0ms (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: 20.1b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize17.0ms (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)
7.8b	(.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))))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`prod-exp_binary64` `add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
8×	`sqrt-prod_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `associate-l_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 90

Calls

4 calls:

20.0ms	(.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))))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(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)))

series842.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

306.0ms	(.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))))
257.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
207.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
71.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5207	2483

prune202.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Merged error: 13.2b

Counts

103 → 7

Compiler

Compiled 3233 to 2599 computations (19.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.9b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.9b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64`
6×	`pow1/2_binary64` `rem-sqrt-square_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`

Counts

4 → 80

Calls

4 calls:

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

series1.6s (12.3%)

Counts

4 → 12

Calls

4 calls:

502.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
499.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
281.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
266.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4956	2472
1	4956	2472

prune263.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	92	7	99

Merged error: 13.2b

Counts

99 → 7

Compiler

Compiled 4744 to 3882 computations (18.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
2.3b	(.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)))
17.0b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
17.0b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`pow1_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`sqrt-prod_binary64`
6×	`cbrt-div_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `associate-l_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-r_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

11.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms	(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)))
9.0ms	(.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 (14.2%)

Counts

4 → 12

Calls

4 calls:

512.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
512.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
502.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
317.0ms	(.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)))

simplify194.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	4888	2839
1	4888	2839

prune262.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	86	7	93

Merged error: 13.2b

Counts

93 → 7

Compiler

Compiled 4480 to 3644 computations (18.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.1b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
11.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64` `cbrt-prod_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`cbrt-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 69

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.4s (10.4%)

Counts

4 → 12

Calls

4 calls:

509.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
323.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
264.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
264.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5029	2301

prune313.0ms (2.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	81	7	88

Merged error: 13.2b

Counts

88 → 7

Compiler

Compiled 5534 to 4552 computations (17.7% saved)

regimes177.0ms (1.4%)

Compiler: Compiled 1664 to 1488 computations (10.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 24 to 22 computations (8.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	152
1	47	152

end0.0ms (0%)

sample3.3s (25.3%)

Algorithm

1×

intervals

Results

1.1s	1415×	body	1280	valid
736.0ms	1322×	body	640	valid
491.0ms	4342×	body	80	valid
231.0ms	589×	body	320	valid
91.0ms	332×	body	160	valid
0.0ms	2×	body	80	invalid

Compiler

Compiled 389 to 341 computations (12.3% saved)

Details

analyze1.8s (13.8%)

sample101.0ms (0.8%)

simplify189.0ms (1.5%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite51.0ms (0.4%)

series842.0ms (6.5%)

simplify100.0ms (0.8%)

prune202.0ms (1.6%)

localize21.0ms (0.2%)

rewrite44.0ms (0.3%)

series1.6s (12.3%)

simplify106.0ms (0.8%)

prune263.0ms (2%)

localize20.0ms (0.2%)

rewrite42.0ms (0.3%)

series1.8s (14.2%)

simplify194.0ms (1.5%)

prune262.0ms (2%)

localize23.0ms (0.2%)

rewrite44.0ms (0.3%)

series1.4s (10.4%)

simplify102.0ms (0.8%)

prune313.0ms (2.4%)

regimes177.0ms (1.4%)

bsearch1.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.3s (25.3%)

Profiling