Details

analyze1.9s (10.4%)

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
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)

sample79.0ms (0.4%)

Algorithm

1×

intervals

Results

33.0ms	58×	body	1024	valid
17.0ms	155×	body	128	valid
11.0ms	28×	body	512	valid
4.0ms	15×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify178.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	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

Error

17.2b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize15.0ms (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))))
8.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite255.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

17.1b

Rules

28×	`add-exp-log_binary64_798`
20×	`pow1_binary64_821`
18×	`add-cbrt-cube_binary64_796`
15×	`*-un-lft-identity_binary64_760`
12×	`add-sqr-sqrt_binary64_782` `prod-exp_binary64_809`
11×	`add-cube-cbrt_binary64_795`
10×	`associate-r_binary64_700`
9×	`pow-prod-down_binary64_831` `cbrt-unprod_binary64_793`
8×	`sqrt-prod_binary64_776`
7×	`unpow-prod-down_binary64_839`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `pow-exp_binary64_828`
3×	`times-frac_binary64_766` `pow-unpow_binary64_837` `div-exp_binary64_811`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-r/_binary64_702` `associate-l_binary64_701` `-commutative_binary64_691`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `div-inv_binary64_757` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `unpow2_binary64_825` `sqr-pow_binary64_732`

Counts

4 → 86

Calls

4 calls:

15.0ms	(.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))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(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)))

Compiler

Compiled 3141 to 2524 computations (19.6% saved)

series1.7s (9.5%)

Error

0.1b

Counts

4 → 55

Calls

4 calls:

734.0ms	(.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))))
465.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
323.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
104.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3909 to 3355 computations (14.2% saved)

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4960	3633
1	4960	3633

prune285.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	8	141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	9	142

Error

0.0b

Counts

142 → 9

Compiler

Compiled 4266 to 3306 computations (22.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
7.1b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite303.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64_821`
29×	`add-exp-log_binary64_798`
20×	`add-cbrt-cube_binary64_796`
19×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
13×	`*-un-lft-identity_binary64_760`
10×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795`
8×	`sqrt-prod_binary64_776`
7×	`associate-r_binary64_700`
6×	`cbrt-prod_binary64_791`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `pow1/3_binary64_842`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 74

Calls

4 calls:

24.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3902 to 3195 computations (18.1% saved)

series1.5s (8.2%)

Error

0.0b

Counts

4 → 47

Calls

4 calls:

750.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
486.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
81.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
72.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4105 to 3494 computations (14.9% saved)

simplify61.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5178	3259

prune315.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	0	7	7
Picked	0	1	1
Done	1	0	1
Total	119	11	130

Error

0.0b

Counts

130 → 11

Compiler

Compiled 4692 to 3741 computations (20.3% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
7.1b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite523.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

58×	`pow1_binary64_821`
57×	`add-exp-log_binary64_798`
42×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
39×	`add-cbrt-cube_binary64_796`
12×	`*-un-lft-identity_binary64_760`
9×	`add-sqr-sqrt_binary64_782`
8×	`add-cube-cbrt_binary64_795` `sqrt-prod_binary64_776`
7×	`associate-r_binary64_700`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `cbrt-prod_binary64_791`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `pow1/3_binary64_842`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 87

Calls

4 calls:

32.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 6221 to 5145 computations (17.3% saved)

series1.5s (8.5%)

Error

0.0b

Counts

4 → 46

Calls

4 calls:

766.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
498.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
87.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
83.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4894 to 4172 computations (14.8% saved)

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4988	5255
1	4988	5255

prune520.0ms (2.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	133	11	144

Error

0.0b

Counts

144 → 11

Compiler

Compiled 6621 to 5398 computations (18.5% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
7.1b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite675.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

91×	`pow1_binary64_821`
90×	`add-exp-log_binary64_798`
70×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
58×	`add-cbrt-cube_binary64_796`
13×	`*-un-lft-identity_binary64_760`
10×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795`
8×	`sqrt-prod_binary64_776`
7×	`associate-r_binary64_700`
6×	`cbrt-prod_binary64_791`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `pow1/3_binary64_842`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 104

Calls

4 calls:

41.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 7649 to 6344 computations (17.1% saved)

series1.6s (8.7%)

Error

0.0b

Counts

4 → 47

Calls

4 calls:

777.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
500.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
89.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
88.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 5125 to 4378 computations (14.6% saved)

simplify121.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4961	4421
1	4961	4421

prune457.0ms (2.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	151	11	162

Error

0.0b

Counts

162 → 11

Compiler

Compiled 6138 to 4942 computations (19.5% saved)

regimes1.1s (6%)

Accuracy

Total 9.1b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 11116 to 9841 computations (11.5% saved)

bsearch4.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	123
1	35	123

end0.0ms (0%)

sample4.8s (26.3%)

Algorithm

1×

intervals

Results

1.2s	1950×	body	1024	valid
545.0ms	4583×	body	128	valid
400.0ms	966×	body	512	valid
140.0ms	501×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 1913 to 1689 computations (11.7% saved)

Details

analyze1.9s (10.4%)

sample79.0ms (0.4%)

simplify178.0ms (1%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite255.0ms (1.4%)

series1.7s (9.5%)

simplify83.0ms (0.5%)

prune285.0ms (1.6%)

localize20.0ms (0.1%)

rewrite303.0ms (1.7%)

series1.5s (8.2%)

simplify61.0ms (0.3%)

prune315.0ms (1.7%)

localize24.0ms (0.1%)

rewrite523.0ms (2.9%)

series1.5s (8.5%)

simplify103.0ms (0.6%)

prune520.0ms (2.9%)

localize24.0ms (0.1%)

rewrite675.0ms (3.7%)

series1.6s (8.7%)

simplify121.0ms (0.7%)

prune457.0ms (2.5%)

regimes1.1s (6%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.8s (26.3%)

Profiling