Details

analyze1.1s (3.8%)

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)

sample223.0ms (0.8%)

Algorithm

1×

intervals

Results

65.0ms	124×	body	1024	valid
59.0ms	130×	body	1024	nan
26.0ms	67×	body	512	valid
25.0ms	76×	body	512	nan
15.0ms	15×	body	2048	valid
8.0ms	31×	body	256	valid
7.0ms	32×	body	256	nan
2.0ms	19×	body	128	valid
1.0ms	1×	body	2048	nan

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify174.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 61.2b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.2b	(*.f64 PI.f64 f)
0.7b	(/.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))))
5.0b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
10×	`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` `associate-l_binary64` `distribute-lft-out--_binary64`
4×	`associate-/l*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 113

Calls

4 calls:

13.0ms	(/.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))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
4.0ms	(*.f64 PI.f64 f)
4.0ms	(*.f64 PI.f64 f)

series344.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

260.0ms	(/.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))))
57.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
14.0ms	(*.f64 PI.f64 f)
13.0ms	(*.f64 PI.f64 f)

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5054	5310

prune320.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Merged error: 1.6b

Counts

126 → 5

Compiler

Compiled 6017 to 4045 computations (32.8% saved)

localize85.0ms (0.3%)

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)

rewrite35.0ms (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:

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

simplify38.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5416	1136

prune1.1s (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 1.6b

Counts

83 → 5

Compiler

Compiled 13963 to 10874 computations (22.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
0.6b	(/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
0.7b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
5.0b	(-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (*.f64 PI.f64 f) 2)))

rewrite233.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

768×	`times-frac_binary64`
723×	`*-un-lft-identity_binary64`
671×	`add-sqr-sqrt_binary64`
252×	`difference-of-squares_binary64`
251×	`add-cube-cbrt_binary64`
194×	`distribute-lft-out_binary64`
189×	`log-prod_binary64`
126×	`sqrt-prod_binary64`
87×	`unpow-prod-down_binary64`
85×	`sqr-pow_binary64`
50×	`associate-/r*_binary64`
42×	`distribute-lft-out--_binary64`
22×	`associate-/r/_binary64`
17×	`add-exp-log_binary64`
14×	`associate-/l*_binary64`
12×	`div-inv_binary64`
11×	`flip3-+_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
7×	`cancel-sign-sub-inv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64`
3×	`rem-log-exp_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `div-sub_binary64` `log-div_binary64`

Counts

4 → 548

Calls

4 calls:

30.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
26.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
16.0ms	(/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
10.0ms	(-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (*.f64 PI.f64 f) 2)))

series1.6s (5.6%)

Counts

4 → 12

Calls

4 calls:

1.0s	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))))
336.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f)))))
158.0ms	(/.f64 (-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (.f64 PI.f64 f) 2))) (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))))
60.0ms	(-.f64 (sqrt.f64 (exp.f64 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 (*.f64 PI.f64 f) 2)))

simplify538.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

560 → 560

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5175	65239

prune3.8s (13.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	556	4	560
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	559	6	565

Merged error: 1.2b

Counts

565 → 6

Compiler

Compiled 45810 to 27561 computations (39.8% saved)

localize208.0ms (0.7%)

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 PI.f64 6)
1.6b	(pow.f64 PI.f64 6)
1.6b	(pow.f64 PI.f64 6)
2.0b	(log.f64 (/.f64 4 (-.f64 (.f64 PI.f64 1/2) (.f64 2 (*.f64 PI.f64 -1/4)))))

rewrite110.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`log-prod_binary64`
10×	`add-exp-log_binary64`
9×	`pow-unpow_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
8×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
2×	`rem-log-exp_binary64` `associate-/r/_binary64`
1×	`flip3--_binary64` `log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 77

Calls

4 calls:

6.0ms	(log.f64 (/.f64 4 (-.f64 (.f64 PI.f64 1/2) (.f64 2 (*.f64 PI.f64 -1/4)))))
2.0ms	(pow.f64 PI.f64 6)
2.0ms	(pow.f64 PI.f64 6)
2.0ms	(pow.f64 PI.f64 6)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(log.f64 (/.f64 4 (-.f64 (.f64 PI.f64 1/2) (.f64 2 (*.f64 PI.f64 -1/4)))))
0.0ms	(pow.f64 PI.f64 6)
0.0ms	(pow.f64 PI.f64 6)
0.0ms	(pow.f64 PI.f64 6)

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5223	3524

prune6.2s (21.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	81	6	87

Merged error: 1.2b

Counts

87 → 6

Compiler

Compiled 52111 to 39157 computations (24.9% saved)

regimes1.7s (5.9%)

Compiler: Compiled 31584 to 23390 computations (25.9% saved)

bsearch0.0ms (0%)

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	1011	1070
1	1011	1070

end0.0ms (0%)

sample10.4s (36.6%)

Algorithm

1×

intervals

Results

1.9s	3852×	body	1024	valid
1.8s	3825×	body	1024	nan
699.0ms	1981×	body	512	valid
627.0ms	1923×	body	512	nan
473.0ms	464×	body	2048	valid
253.0ms	1036×	body	256	valid
197.0ms	902×	body	256	nan
87.0ms	667×	body	128	valid
2.0ms	3×	body	2048	nan
0.0ms	2×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 5910 to 4390 computations (25.7% saved)

Details

analyze1.1s (3.8%)

sample223.0ms (0.8%)

simplify174.0ms (0.6%)

prune8.0ms (0%)

localize25.0ms (0.1%)

rewrite45.0ms (0.2%)

series344.0ms (1.2%)

simplify104.0ms (0.4%)

prune320.0ms (1.1%)

localize85.0ms (0.3%)

rewrite35.0ms (0.1%)

series0.0ms (0%)

simplify38.0ms (0.1%)

prune1.1s (3.8%)

localize22.0ms (0.1%)

rewrite233.0ms (0.8%)

series1.6s (5.6%)

simplify538.0ms (1.9%)

prune3.8s (13.4%)

localize208.0ms (0.7%)

rewrite110.0ms (0.4%)

series0.0ms (0%)

simplify64.0ms (0.2%)

prune6.2s (21.8%)

regimes1.7s (5.9%)

bsearch0.0ms (0%)

simplify29.0ms (0.1%)

end0.0ms (0%)

sample10.4s (36.6%)

Profiling