Details

analyze1.1s (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample214.0ms (0.3%)

Algorithm

1×

intervals

Results

65.0ms	127×	body	1024	valid
50.0ms	108×	body	1024	nan
28.0ms	76×	body	512	nan
21.0ms	58×	body	512	valid
16.0ms	14×	body	2048	valid
8.0ms	31×	body	256	valid
7.0ms	29×	body	256	nan
3.0ms	26×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify179.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune10.0ms (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: 61.0b

Counts

2 → 2

Compiler

Compiled 101 to 78 computations (22.8% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
1.5b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
6.5b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite64.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`unpow-prod-down_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/r*_binary64` `sqr-pow_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
3×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 141

Calls

4 calls:

21.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
9.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

series370.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
58.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
25.0ms	(*.f64 (/.f64 PI.f64 4) f)
23.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5184	5751

prune1.0s (1.3%)

Pruning

46 alts after pruning (45 fresh and 1 done)

	Pruned	Kept	Total
New	108	45	153
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	109	46	155

Merged error: 2.0b

Counts

155 → 46

Compiler

Compiled 7657 to 5315 computations (30.6% saved)

localize87.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 PI.f64 3)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)

rewrite41.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`pow-unpow_binary64` `unpow-prod-down_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
3×	`cube-prod_binary64`
1×	`rem-cube-cbrt_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 74

Calls

4 calls:

3.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 3)
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 3)

simplify41.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5373	1148

prune1.2s (1.5%)

Pruning

55 alts after pruning (53 fresh and 2 done)

	Pruned	Kept	Total
New	69	9	78
Fresh	0	44	44
Picked	0	1	1
Done	0	1	1
Total	69	55	124

Merged error: 2.0b

Counts

124 → 55

Compiler

Compiled 12418 to 9656 computations (22.2% saved)

localize97.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (cbrt.f64 PI.f64) 4)
2.0b	(pow.f64 (cbrt.f64 PI.f64) 8)

rewrite40.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`unpow-prod-down_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`pow-unpow_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
6×	`pow-pow_binary64` `cbrt-prod_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
2×	`pow1/3_binary64`

Counts

4 → 76

Calls

4 calls:

3.0ms	(pow.f64 (cbrt.f64 PI.f64) 8)
3.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
3.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 (cbrt.f64 PI.f64) 8)
0.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)

simplify43.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4911	1170
1	4911	1170

prune1.7s (2.2%)

Pruning

67 alts after pruning (64 fresh and 3 done)

	Pruned	Kept	Total
New	67	13	80
Fresh	1	51	52
Picked	0	1	1
Done	0	2	2
Total	68	67	135

Merged error: 2.0b

Counts

135 → 67

Compiler

Compiled 15998 to 12373 computations (22.7% saved)

localize100.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (cbrt.f64 PI.f64) 4)
2.0b	(pow.f64 (cbrt.f64 PI.f64) 8)

rewrite37.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`unpow-prod-down_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`pow-unpow_binary64` `cbrt-prod_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
5×	`pow-pow_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `pow1/3_binary64` `sqr-pow_binary64` `pow-exp_binary64`

Counts

4 → 70

Calls

4 calls:

3.0ms	(pow.f64 (cbrt.f64 PI.f64) 8)
3.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
2.0ms	(pow.f64 PI.f64 4)
1.0ms	(cbrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 (cbrt.f64 PI.f64) 8)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
0.0ms	(cbrt.f64 PI.f64)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4877	1127
1	4877	1127

prune1.8s (2.3%)

Pruning

72 alts after pruning (68 fresh and 4 done)

	Pruned	Kept	Total
New	65	9	74
Fresh	4	59	63
Picked	0	1	1
Done	0	3	3
Total	69	72	141

Merged error: 2.0b

Counts

141 → 72

Compiler

Compiled 9876 to 7661 computations (22.4% saved)

regimes9.8s (12.4%)

Compiler: Compiled 193338 to 151988 computations (21.4% saved)

bsearch26.5s (33.7%)

simplify23.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	156	121
1	156	121

end0.0ms (0%)

sample34.0s (43.3%)

Algorithm

1×

intervals

Results

1.9s	3836×	body	1024	valid
1.8s	3821×	body	1024	nan
728.0ms	2017×	body	512	valid
639.0ms	1928×	body	512	nan
519.0ms	495×	body	2048	valid
254.0ms	1001×	body	256	valid
217.0ms	978×	body	256	nan
85.0ms	651×	body	128	valid
2.0ms	3×	body	2048	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 33205 to 26090 computations (21.4% saved)

Pareto

1.5309764377586171e-06

Details

analyze1.1s (1.4%)

sample214.0ms (0.3%)

simplify179.0ms (0.2%)

prune10.0ms (0%)

localize18.0ms (0%)

rewrite64.0ms (0.1%)

series370.0ms (0.5%)

simplify79.0ms (0.1%)

prune1.0s (1.3%)

localize87.0ms (0.1%)

rewrite41.0ms (0.1%)

series0.0ms (0%)

simplify41.0ms (0.1%)

prune1.2s (1.5%)

localize97.0ms (0.1%)

rewrite40.0ms (0.1%)

series0.0ms (0%)

simplify43.0ms (0.1%)

prune1.7s (2.2%)

localize100.0ms (0.1%)

rewrite37.0ms (0%)

series0.0ms (0%)

simplify72.0ms (0.1%)

prune1.8s (2.3%)

regimes9.8s (12.4%)

bsearch26.5s (33.7%)

simplify23.0ms (0%)

end0.0ms (0%)

sample34.0s (43.3%)

Profiling