Details

analyze1.1s (7.5%)

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)

sample244.0ms (1.7%)

Algorithm

1×

intervals

Results

72.0ms	138×	body	1024	nan
70.0ms	129×	body	1024	valid
27.0ms	70×	body	512	nan
27.0ms	69×	body	512	valid
16.0ms	13×	body	2048	valid
7.0ms	28×	body	256	nan
7.0ms	25×	body	256	valid
3.0ms	20×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify253.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4782	55
1	4782	55

prune15.0ms (0.1%)

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: 61.9b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(*.f64 (/.f64 PI.f64 4) f)
1.0b	(/.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))))
4.9b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `sqr-pow_binary64` `unpow-prod-down_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 → 134

Calls

4 calls:

15.0ms	(/.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)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

series640.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

459.0ms	(/.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))))
93.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
48.0ms	(*.f64 (/.f64 PI.f64 4) f)
39.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5234	5639

prune423.0ms (2.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	3	147

Merged error: 1.4b

Counts

147 → 3

Compiler

Compiled 6765 to 4581 computations (32.3% saved)

localize89.0ms (0.6%)

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)

rewrite40.0ms (0.3%)

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)
3.0ms	(pow.f64 PI.f64 3)
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 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 (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5295	1148

prune1.1s (7.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Merged error: 1.4b

Counts

81 → 3

Compiler

Compiled 14032 to 11021 computations (21.5% saved)

localize102.0ms (0.7%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`
16×	`unpow-prod-down_binary64`
13×	`pow1_binary64`
12×	`pow-unpow_binary64`
10×	`add-exp-log_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `pow-exp_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`pow-pow_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
5.0ms	(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.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 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
0.0ms	(pow.f64 PI.f64 4)

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5041	1121

prune1.8s (12.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	104	3	107

Merged error: 1.4b

Counts

107 → 3

Compiler

Compiled 19635 to 15630 computations (20.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(*.f64 (/.f64 PI.f64 4) f)
1.0b	(/.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))))
4.9b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite61.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `sqr-pow_binary64` `unpow-prod-down_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 → 134

Calls

4 calls:

15.0ms	(/.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))))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

series553.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

417.0ms	(/.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))))
62.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
37.0ms	(*.f64 (/.f64 PI.f64 4) f)
36.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5234	5639

prune413.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	146	3	149

Merged error: 1.4b

Counts

149 → 3

Compiler

Compiled 6952 to 4821 computations (30.7% saved)

regimes33.0ms (0.2%)

Compiler: Compiled 260 to 207 computations (20.4% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	314	307
1	314	307

end0.0ms (0%)

sample7.4s (50.4%)

Algorithm

1×

intervals

Results

2.1s	3847×	body	1024	valid
2.0s	4024×	body	1024	nan
747.0ms	1954×	body	512	valid
668.0ms	1908×	body	512	nan
573.0ms	503×	body	2048	valid
266.0ms	1009×	body	256	valid
227.0ms	956×	body	256	nan
97.0ms	687×	body	128	valid
5.0ms	6×	body	2048	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 481 to 386 computations (19.8% saved)

Details

analyze1.1s (7.5%)

sample244.0ms (1.7%)

simplify253.0ms (1.7%)

prune15.0ms (0.1%)

localize20.0ms (0.1%)

rewrite58.0ms (0.4%)

series640.0ms (4.4%)

simplify78.0ms (0.5%)

prune423.0ms (2.9%)

localize89.0ms (0.6%)

rewrite40.0ms (0.3%)

series0.0ms (0%)

simplify41.0ms (0.3%)

prune1.1s (7.6%)

localize102.0ms (0.7%)

rewrite59.0ms (0.4%)

series0.0ms (0%)

simplify55.0ms (0.4%)

prune1.8s (12.1%)

localize21.0ms (0.1%)

rewrite61.0ms (0.4%)

series553.0ms (3.8%)

simplify80.0ms (0.5%)

prune413.0ms (2.8%)

regimes33.0ms (0.2%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample7.4s (50.4%)

Profiling