Details

analyze1.1s (7.4%)

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 (1.5%)

Algorithm

1×

intervals

Results

65.0ms	128×	body	1024	valid
56.0ms	116×	body	1024	nan
23.0ms	64×	body	512	valid
23.0ms	22×	body	2048	valid
16.0ms	47×	body	512	nan
7.0ms	30×	body	256	nan
6.0ms	23×	body	256	valid
3.0ms	19×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify181.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune8.0ms (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: 61.5b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize17.0ms (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)
1.2b	(/.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))))
4.0b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite65.0ms (0.4%)

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:

14.0ms	(/.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)

series262.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(/.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))))
55.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
33.0ms	(*.f64 (/.f64 PI.f64 4) f)
33.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 872 to 682 computations (21.8% saved)

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5266	5387

prune396.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	146	7	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	7	154

Merged error: 2.1b

Counts

154 → 7

Compiler

Compiled 6871 to 4605 computations (33% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (.f64 1/2 f)))
0.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))
1.2b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (.f64 1/2 f))))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
33×	`add-exp-log_binary64`
30×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
23×	`add-cbrt-cube_binary64`
17×	`associate-l_binary64`
16×	`associate-r_binary64`
10×	`pow1_binary64` `prod-exp_binary64`
8×	`log-prod_binary64` `div-exp_binary64`
7×	`cbrt-unprod_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `div-inv_binary64`
3×	`distribute-lft-out_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `log-pow_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

4 → 113

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (.f64 1/2 f)))
10.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (.f64 1/2 f))))
9.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

series456.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))
161.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (.f64 1/2 f))))
69.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 (.f64 1/2 f)))
28.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 582 to 479 computations (17.7% saved)

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5411	3931

prune258.0ms (1.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	114	11	125
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	116	16	132

Merged error: 1.7b

Counts

132 → 16

Compiler

Compiled 4607 to 3157 computations (31.5% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
1.0b	(cbrt.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 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (*.f64 f 1/2)))
1.2b	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
18×	`log-prod_binary64`
16×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64`
7×	`times-frac_binary64`
6×	`cbrt-div_binary64` `pow1_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `log-pow_binary64` `log-div_binary64` `flip-+_binary64`
2×	`div-exp_binary64`
1×	`prod-exp_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

9.0ms	(log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (*.f64 f 1/2)))
7.0ms	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
6.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
6.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))

series922.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

390.0ms	(log.f64 (/.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (*.f64 f 1/2)))
234.0ms	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
150.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
148.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))

Compiler

Compiled 1120 to 917 computations (18.1% saved)

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5490	2860

prune256.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	85	13	98

Merged error: 1.6b

Counts

98 → 13

Compiler

Compiled 4836 to 3366 computations (30.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (log.f64 PI.f64)) (log.f64 (/.f64 (cbrt.f64 2) (*.f64 f 1/2)))) (/.f64 -4 PI.f64))
1.0b	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
1.0b	(cbrt.f64 2)
1.2b	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`
11×	`cbrt-prod_binary64`
10×	`add-exp-log_binary64` `times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`log-prod_binary64`
5×	`associate-l_binary64`
4×	`cbrt-div_binary64` `flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
3×	`pow1/3_binary64` `log-pow_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `log-div_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

18.0ms	(.f64 (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (log.f64 PI.f64)) (log.f64 (/.f64 (cbrt.f64 2) (*.f64 f 1/2)))) (/.f64 -4 PI.f64))
6.0ms	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
6.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
1.0ms	(cbrt.f64 2)

series940.0ms (6.4%)

Counts

4 → 11

Calls

4 calls:

574.0ms	(.f64 (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))) (log.f64 PI.f64)) (log.f64 (/.f64 (cbrt.f64 2) (*.f64 f 1/2)))) (/.f64 -4 PI.f64))
229.0ms	(log.f64 (cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
137.0ms	(cbrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
0.0ms	(cbrt.f64 2)

Compiler

Compiled 784 to 681 computations (13.1% saved)

simplify86.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4935	4240
1	4935	4240

prune227.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	92	14	106

Merged error: 1.6b

Counts

106 → 14

Compiler

Compiled 4014 to 2917 computations (27.3% saved)

regimes725.0ms (4.9%)

Compiler: Compiled 11442 to 8858 computations (22.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	65
1	50	65

end0.0ms (0%)

sample8.1s (55.5%)

Algorithm

1×

intervals

Results

2.0s	3882×	body	1024	valid
1.8s	3873×	body	1024	nan
715.0ms	1966×	body	512	valid
632.0ms	1897×	body	512	nan
514.0ms	501×	body	2048	valid
239.0ms	977×	body	256	valid
217.0ms	952×	body	256	nan
87.0ms	674×	body	128	valid
5.0ms	5×	body	2048	nan
1.0ms	5×	body	128	nan
0.0ms	4×	body	128	overflowed

Compiler

Compiled 1937 to 1504 computations (22.4% saved)

Details

analyze1.1s (7.4%)

sample214.0ms (1.5%)

simplify181.0ms (1.2%)

prune8.0ms (0.1%)

localize17.0ms (0.1%)

rewrite65.0ms (0.4%)

series262.0ms (1.8%)

simplify96.0ms (0.7%)

prune396.0ms (2.7%)

localize17.0ms (0.1%)

rewrite52.0ms (0.4%)

series456.0ms (3.1%)

simplify65.0ms (0.4%)

prune258.0ms (1.8%)

localize28.0ms (0.2%)

rewrite37.0ms (0.3%)

series922.0ms (6.3%)

simplify73.0ms (0.5%)

prune256.0ms (1.7%)

localize24.0ms (0.2%)

rewrite41.0ms (0.3%)

series940.0ms (6.4%)

simplify86.0ms (0.6%)

prune227.0ms (1.5%)

regimes725.0ms (4.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.1s (55.5%)

Profiling