Details

analyze1.1s (5.6%)

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)

sample231.0ms (1.2%)

Algorithm

1×

intervals

Results

73.0ms	127×	body	1024	valid
56.0ms	109×	body	1024	nan
27.0ms	70×	body	512	valid
26.0ms	73×	body	512	nan
17.0ms	14×	body	2048	valid
7.0ms	24×	body	256	valid
7.0ms	26×	body	256	nan
3.0ms	21×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify250.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4782	55
1	4782	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: 61.4b

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)
0.3b	(log.f64 (/.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)))))
1.2b	(/.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))))
6.0b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite78.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`
30×	`difference-of-squares_binary64`
15×	`distribute-lft-out_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`
11×	`add-cbrt-cube_binary64`
10×	`sqr-pow_binary64` `unpow-prod-down_binary64` `distribute-lft-out--_binary64`
7×	`associate-/r*_binary64` `pow1_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 147

Calls

4 calls:

21.0ms	(log.f64 (/.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)))))
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))))
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)

series2.1s (11%)

Counts

4 → 12

Calls

4 calls:

1.5s	(log.f64 (/.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)))))
458.0ms	(/.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))))
80.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
38.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify133.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4969	9836
1	4969	9836

prune588.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	154	5	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	5	160

Merged error: 1.8b

Counts

160 → 5

Compiler

Compiled 9043 to 6230 computations (31.1% saved)

localize88.0ms (0.5%)

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)

rewrite39.0ms (0.2%)

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)

simplify40.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5213	1424

prune1.2s (6.4%)

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: 1.8b

Counts

83 → 5

Compiler

Compiled 15145 to 12019 computations (20.6% saved)

localize219.0ms (1.1%)

Local error

Found 4 expressions with local error:

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

rewrite86.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64`
14×	`pow1_binary64`
9×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
7×	`log-prod_binary64`
6×	`pow-pow_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
2×	`div-exp_binary64`
1×	`log-pow_binary64` `div-inv_binary64` `log-div_binary64`

Counts

4 → 70

Calls

4 calls:

6.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
5.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))
5.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

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

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	6065	3502

prune3.5s (18.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Merged error: 1.8b

Counts

79 → 5

Compiler

Compiled 35466 to 26161 computations (26.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
1.2b	(log.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
1.2b	(log.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
6.0b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `log-prod_binary64`
10×	`pow1_binary64` `difference-of-squares_binary64`
8×	`add-cube-cbrt_binary64` `log-div_binary64`
7×	`associate--r+_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `log-pow_binary64` `add-exp-log_binary64`
4×	`flip3--_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `associate--l+_binary64`
3×	`sqr-pow_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `associate--l-_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `flip-+_binary64`

Counts

4 → 79

Calls

4 calls:

16.0ms	(-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
7.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(log.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
6.0ms	(log.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))

series1.1s (5.9%)

Counts

4 → 12

Calls

4 calls:

587.0ms	(-.f64 (log.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (log.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
294.0ms	(log.f64 (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
178.0ms	(log.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
72.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5267	4377

prune237.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	90	6	96

Merged error: 1.7b

Counts

96 → 6

Compiler

Compiled 4343 to 2946 computations (32.2% saved)

regimes127.0ms (0.7%)

Compiler: Compiled 931 to 703 computations (24.5% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	320	307
1	320	307

end0.0ms (0%)

sample7.8s (40.5%)

Algorithm

1×

intervals

Results

2.1s	3966×	body	1024	valid
1.9s	3808×	body	1024	nan
729.0ms	1891×	body	512	valid
679.0ms	1896×	body	512	nan
556.0ms	488×	body	2048	valid
271.0ms	976×	body	256	valid
238.0ms	985×	body	256	nan
102.0ms	679×	body	128	valid
6.0ms	6×	body	2048	nan
0.0ms	3×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 1153 to 883 computations (23.4% saved)

Details

analyze1.1s (5.6%)

sample231.0ms (1.2%)

simplify250.0ms (1.3%)

prune8.0ms (0%)

localize20.0ms (0.1%)

rewrite78.0ms (0.4%)

series2.1s (11%)

simplify133.0ms (0.7%)

prune588.0ms (3.1%)

localize88.0ms (0.5%)

rewrite39.0ms (0.2%)

series0.0ms (0%)

simplify40.0ms (0.2%)

prune1.2s (6.4%)

localize219.0ms (1.1%)

rewrite86.0ms (0.4%)

series0.0ms (0%)

simplify67.0ms (0.4%)

prune3.5s (18.4%)

localize19.0ms (0.1%)

rewrite51.0ms (0.3%)

series1.1s (5.9%)

simplify66.0ms (0.3%)

prune237.0ms (1.2%)

regimes127.0ms (0.7%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample7.8s (40.5%)

Profiling