Details

analyze1.1s (7.9%)

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 (1.6%)

Algorithm

1×

intervals

Results

67.0ms	120×	body	1024	valid
50.0ms	98×	body	1024	nan
28.0ms	69×	body	512	nan
25.0ms	62×	body	512	valid
21.0ms	16×	body	2048	valid
9.0ms	32×	body	256	valid
7.0ms	27×	body	256	nan
4.0ms	26×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify241.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4782	55
1	4782	55

prune8.0ms (0.1%)

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: 60.7b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.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))))
7.3b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite57.0ms (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:

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))))
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)

series616.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

444.0ms	(/.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)))
40.0ms	(*.f64 (/.f64 PI.f64 4) f)
38.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5234	5639

prune397.0ms (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: 1.6b

Counts

147 → 4

Compiler

Compiled 6832 to 4633 computations (32.2% saved)

localize84.0ms (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)

rewrite42.0ms (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 4)
3.0ms	(pow.f64 PI.f64 3)

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

prune997.0ms (7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Merged error: 1.6b

Counts

82 → 4

Compiler

Compiled 13914 to 10924 computations (21.5% saved)

localize48.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 f (pow.f64 PI.f64 2))
1.0b	(pow.f64 PI.f64 3)
1.0b	(pow.f64 PI.f64 3)
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 (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 f (+.f64 (.f64 PI.f64 1/4) (.f64 1/32 (.f64 f (pow.f64 PI.f64 2)))))) (-.f64 (-.f64 (.f64 PI.f64 (.f64 f 1/4)) (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64)))) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16)))))))

rewrite69.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`log-prod_binary64`
22×	`add-cube-cbrt_binary64`
16×	`times-frac_binary64`
14×	`add-exp-log_binary64`
10×	`unpow-prod-down_binary64`
8×	`distribute-lft-out_binary64` `associate-r_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `associate-/r/_binary64` `cube-prod_binary64`
4×	`add-log-exp_binary64` `frac-add_binary64` `sqr-pow_binary64` `unswap-sqr_binary64`
3×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-l_binary64` `prod-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
2×	`flip3--_binary64` `unpow2_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-unprod_binary64` `log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64` `*-commutative_binary64`

Counts

4 → 110

Calls

4 calls:

32.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 f (+.f64 (.f64 PI.f64 1/4) (.f64 1/32 (.f64 f (pow.f64 PI.f64 2)))))) (-.f64 (-.f64 (.f64 PI.f64 (.f64 f 1/4)) (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64)))) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16)))))))
6.0ms	(*.f64 f (pow.f64 PI.f64 2))
2.0ms	(pow.f64 PI.f64 3)
2.0ms	(pow.f64 PI.f64 3)

series566.0ms (4%)

Counts

4 → 8

Calls

4 calls:

524.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 f (+.f64 (.f64 PI.f64 1/4) (.f64 1/32 (.f64 f (pow.f64 PI.f64 2)))))) (-.f64 (-.f64 (.f64 PI.f64 (.f64 f 1/4)) (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64)))) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16)))))))
42.0ms	(*.f64 f (pow.f64 PI.f64 2))
0.0ms	(pow.f64 PI.f64 3)
0.0ms	(pow.f64 PI.f64 3)

simplify107.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4984	8631
1	4984	8631

prune816.0ms (5.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	111	11	122

Merged error: 1.4b

Counts

122 → 11

Compiler

Compiled 12061 to 8762 computations (27.4% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 f (pow.f64 PI.f64 2))
0.4b	(*.f64 f (pow.f64 PI.f64 2))
0.4b	(*.f64 f (pow.f64 PI.f64 2))
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
24×	`associate-r_binary64`
22×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`log-prod_binary64`
12×	`unswap-sqr_binary64` `unpow-prod-down_binary64`
10×	`add-cbrt-cube_binary64`
9×	`associate-l_binary64` `prod-exp_binary64` `times-frac_binary64`
6×	`unpow2_binary64` `sqr-pow_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
2×	`rem-log-exp_binary64`
1×	`log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 105

Calls

4 calls:

6.0ms	(*.f64 f (pow.f64 PI.f64 2))
6.0ms	(*.f64 f (pow.f64 PI.f64 2))
6.0ms	(*.f64 f (pow.f64 PI.f64 2))
3.0ms	(log.f64 (/.f64 4 PI.f64))

series140.0ms (1%)

Counts

4 → 10

Calls

4 calls:

51.0ms	(*.f64 f (pow.f64 PI.f64 2))
44.0ms	(*.f64 f (pow.f64 PI.f64 2))
43.0ms	(*.f64 f (pow.f64 PI.f64 2))
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5024	1228

prune356.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	115	11	126

Merged error: 1.4b

Counts

126 → 11

Compiler

Compiled 6956 to 4689 computations (32.6% saved)

regimes100.0ms (0.7%)

Compiler: Compiled 1177 to 896 computations (23.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	162	93
1	162	93

end0.0ms (0%)

sample7.9s (55.8%)

Algorithm

1×

intervals

Results

2.1s	3823×	body	1024	valid
1.9s	3837×	body	1024	nan
778.0ms	1990×	body	512	valid
726.0ms	2012×	body	512	nan
607.0ms	517×	body	2048	valid
271.0ms	1009×	body	256	valid
240.0ms	963×	body	256	nan
95.0ms	661×	body	128	valid
3.0ms	4×	body	2048	nan
0.0ms	2×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 1270 to 969 computations (23.7% saved)

Details

analyze1.1s (7.9%)

sample227.0ms (1.6%)

simplify241.0ms (1.7%)

prune8.0ms (0.1%)

localize27.0ms (0.2%)

rewrite57.0ms (0.4%)

series616.0ms (4.3%)

simplify75.0ms (0.5%)

prune397.0ms (2.8%)

localize84.0ms (0.6%)

rewrite42.0ms (0.3%)

series0.0ms (0%)

simplify39.0ms (0.3%)

prune997.0ms (7%)

localize48.0ms (0.3%)

rewrite69.0ms (0.5%)

series566.0ms (4%)

simplify107.0ms (0.8%)

prune816.0ms (5.7%)

localize33.0ms (0.2%)

rewrite39.0ms (0.3%)

series140.0ms (1%)

simplify82.0ms (0.6%)

prune356.0ms (2.5%)

regimes100.0ms (0.7%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.9s (55.8%)

Profiling