Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample54.0ms (0.9%)

Algorithm

1×

intervals

Results

22.0ms	68×	body	2048	valid
10.0ms	47×	body	1024	valid
7.0ms	123×	body	128	valid
2.0ms	13×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify164.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (0.1%)

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

Error

17.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0b	(atan.f64 (+.f64 N 1))
0.0b	(atan.f64 (+.f64 N 1))
1.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1092` `*-un-lft-identity_binary64_1070`
4×	`add-log-exp_binary64_1109`
3×	`cancel-sign-sub-inv_binary64_1036` `add-cube-cbrt_binary64_1105`
2×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `pow1_binary64_1131`
1×	`diff-atan_binary64_1227` `flip--_binary64_1045` `flip3--_binary64_1074` `distribute-lft-out--_binary64_1022` `difference-of-squares_binary64_1039` `sub-neg_binary64_1063` `diff-log_binary64_1162`

Counts

2 → 24

Calls

4 calls:

7.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
2.0ms	(atan.f64 (+.f64 N 1))
0.0ms	(atan.f64 (+.f64 N 1))
0.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series57.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

43.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
14.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 84 to 72 computations (14.3% saved)

simplify131.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune45.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	1	31

Error

0.5b

Counts

31 → 1

Compiler

Compiled 351 to 229 computations (34.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0b	(*.f64 N (+.f64 N 1))
0.0b	(*.f64 N (+.f64 N 1))
0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1092` `*-un-lft-identity_binary64_1070`
4×	`associate-r_binary64_1010` `add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `pow1_binary64_1131` `add-cube-cbrt_binary64_1105`
3×	`associate-l_binary64_1011`
2×	`associate-*r/_binary64_1012` `add-log-exp_binary64_1109`
1×	`cbrt-unprod_binary64_1103` `*-commutative_binary64_1001` `flip-+_binary64_1044` `distribute-lft-out_binary64_1021` `prod-exp_binary64_1119` `unswap-sqr_binary64_1038` `pow-prod-down_binary64_1141` `distribute-rgt-in_binary64_1020` `flip3-+_binary64_1073` `distribute-lft-in_binary64_1019`

Counts

2 → 30

Calls

4 calls:

11.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms	(*.f64 N (+.f64 N 1))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series89.0ms (1.4%)

Counts

2 → 9

Calls

2 calls:

60.0ms	(*.f64 N (+.f64 N 1))
29.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 127 to 115 computations (9.4% saved)

simplify134.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4927	392
1	4927	392

prune110.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Error

0.5b

Counts

40 → 7

Compiler

Compiled 613 to 477 computations (22.2% saved)

localize20.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.5b	(cbrt.f64 N)
0.5b	(cbrt.f64 N)
0.2b	(.f64 (.f64 (cbrt.f64 N) (cbrt.f64 N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))
0.1b	(*.f64 (+.f64 1 N) (cbrt.f64 N))
0.5b	(cbrt.f64 N)
0.5b	(cbrt.f64 N)
0.5b	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
0.5b	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 N) (cbrt.f64 N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1092` `cbrt-prod_binary64_1101`
14×	`*-un-lft-identity_binary64_1070` `add-cube-cbrt_binary64_1105`
11×	`pow1_binary64_1131`
8×	`pow1/3_binary64_1152`
6×	`associate-r_binary64_1010` `add-exp-log_binary64_1108` `swap-sqr_binary64_1037` `associate-l_binary64_1011`
4×	`add-cbrt-cube_binary64_1106` `unswap-sqr_binary64_1038` `add-log-exp_binary64_1109`
2×	`pow-sqr_binary64_1043` `pow-prod-up_binary64_1140` `pow-prod-down_binary64_1141`
1×	`pow-plus_binary64_1133` `cbrt-unprod_binary64_1103` `*-commutative_binary64_1001` `pow2_binary64_1151` `prod-exp_binary64_1119`

Counts

4 → 69

Calls

8 calls:

12.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
2.0ms	(cbrt.f64 N)
2.0ms	(cbrt.f64 N)
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 N) (cbrt.f64 N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))
0.0ms	(*.f64 (+.f64 1 N) (cbrt.f64 N))

series453.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
134.0ms	(cbrt.f64 N)
125.0ms	(cbrt.f64 N)
39.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 N) (cbrt.f64 N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))

Compiler

Compiled 404 to 338 computations (16.3% saved)

simplify165.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	4955	635
1	4955	635

prune159.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	81	7	88

Error

0.5b

Counts

88 → 7

Compiler

Compiled 1572 to 955 computations (39.2% saved)

localize21.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))
0.0b	(*.f64 N (+.f64 1 N))
0.0b	(*.f64 N (+.f64 1 N))
0.0b	(*.f64 N (+.f64 1 N))
0.5b	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))))
15.5b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
15.5b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
15.5b	(cbrt.f64 (*.f64 N (+.f64 1 N)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-*r/_binary64_1012` `cbrt-div_binary64_1102`
4×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `add-sqr-sqrt_binary64_1092` `add-log-exp_binary64_1109` `pow1_binary64_1131` `*-un-lft-identity_binary64_1070` `add-cube-cbrt_binary64_1105`
3×	`flip-+_binary64_1044` `flip3-+_binary64_1073` `cbrt-prod_binary64_1101` `pow1/3_binary64_1152`

Counts

4 → 40

Calls

8 calls:

8.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
8.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
8.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))))
0.0ms	(*.f64 N (+.f64 1 N))

series366.0ms (5.9%)

Counts

4 → 30

Calls

4 calls:

112.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
108.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
103.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
42.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))))

Compiler

Compiled 1166 to 998 computations (14.4% saved)

simplify158.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4818	1125
1	4818	1125

prune187.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	71	6	77

Error

0.5b

Counts

77 → 6

Compiler

Compiled 1960 to 1456 computations (25.7% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	116	375
1	116	375

regimes62.0ms (1%)

Accuracy

Total 0.0b remaining (13.7%)

Threshold costs 0.0b (13.7%)

Compiler

Compiled 251 to 210 computations (16.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample3.6s (59.2%)

Algorithm

1×

intervals

Results

692.0ms	2131×	body	2048	valid
256.0ms	4109×	body	128	valid
232.0ms	1032×	body	1024	valid
85.0ms	488×	body	512	valid
29.0ms	240×	body	256	valid

Compiler

Compiled 765 to 641 computations (16.2% saved)

Pareto

0.6335447833927076

Details

analyze2.0ms (0%)

sample54.0ms (0.9%)

simplify164.0ms (2.7%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite12.0ms (0.2%)

series57.0ms (0.9%)

simplify131.0ms (2.1%)

prune45.0ms (0.7%)

localize12.0ms (0.2%)

rewrite16.0ms (0.3%)

series89.0ms (1.4%)

simplify134.0ms (2.2%)

prune110.0ms (1.8%)

localize20.0ms (0.3%)

rewrite27.0ms (0.4%)

series453.0ms (7.4%)

simplify165.0ms (2.7%)

prune159.0ms (2.6%)

localize21.0ms (0.3%)

rewrite33.0ms (0.5%)

series366.0ms (5.9%)

simplify158.0ms (2.6%)

prune187.0ms (3%)

simplify12.0ms (0.2%)

regimes62.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.6s (59.2%)

Profiling