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)

sample227.0ms (1.5%)

Algorithm

1×

intervals

Results

62.0ms	111×	body	1024	nan
60.0ms	109×	body	1024	valid
29.0ms	75×	body	512	valid
22.0ms	61×	body	512	nan
19.0ms	16×	body	2048	valid
9.0ms	34×	body	256	valid
7.0ms	26×	body	256	nan
3.0ms	22×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify247.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4782	55
1	4782	55

prune9.0ms (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: 61.3b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize27.0ms (0.2%)

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))))
5.6b	(-.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)

series621.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

447.0ms	(/.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)))
42.0ms	(*.f64 (/.f64 PI.f64 4) f)
38.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5234	5639

prune419.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	4	147

Merged error: 1.4b

Counts

147 → 4

Compiler

Compiled 6862 to 4653 computations (32.2% saved)

localize85.0ms (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)

rewrite38.0ms (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 4)
3.0ms	(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)

simplify39.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5295	1148

prune1.0s (6.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	78	4	82

Merged error: 1.4b

Counts

82 → 4

Compiler

Compiled 14129 to 11093 computations (21.5% saved)

localize98.0ms (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))

rewrite56.0ms (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)

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5041	1121

prune1.8s (12.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	104	4	108

Merged error: 1.4b

Counts

108 → 4

Compiler

Compiled 19923 to 15857 computations (20.4% saved)

localize100.0ms (0.7%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 2)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (pow.f64 PI.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 4))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

5.0ms	(pow.f64 (pow.f64 PI.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 4))
3.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(cbrt.f64 2)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 (pow.f64 PI.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 4))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(cbrt.f64 2)
0.0ms	(pow.f64 PI.f64 4)

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5028	1447

prune1.1s (7.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Merged error: 1.4b

Counts

79 → 4

Compiler

Compiled 14045 to 11209 computations (20.2% saved)

regimes41.0ms (0.3%)

Compiler: Compiled 371 to 293 computations (21% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	323	331
1	323	331

end0.0ms (0%)

sample7.5s (50.7%)

Algorithm

1×

intervals

Results

2.1s	3929×	body	1024	valid
2.0s	3875×	body	1024	nan
769.0ms	1973×	body	512	valid
673.0ms	1894×	body	512	nan
570.0ms	488×	body	2048	valid
260.0ms	962×	body	256	valid
236.0ms	983×	body	256	nan
95.0ms	648×	body	128	valid
2.0ms	3×	body	2048	nan
0.0ms	2×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 606 to 486 computations (19.8% saved)

Details

analyze1.1s (7.5%)

sample227.0ms (1.5%)

simplify247.0ms (1.7%)

prune9.0ms (0.1%)

localize27.0ms (0.2%)

rewrite58.0ms (0.4%)

series621.0ms (4.2%)

simplify77.0ms (0.5%)

prune419.0ms (2.8%)

localize85.0ms (0.6%)

rewrite38.0ms (0.3%)

series0.0ms (0%)

simplify39.0ms (0.3%)

prune1.0s (6.8%)

localize98.0ms (0.7%)

rewrite56.0ms (0.4%)

series0.0ms (0%)

simplify53.0ms (0.4%)

prune1.8s (12.2%)

localize100.0ms (0.7%)

rewrite41.0ms (0.3%)

series0.0ms (0%)

simplify40.0ms (0.3%)

prune1.1s (7.5%)

regimes41.0ms (0.3%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample7.5s (50.7%)

Profiling