Details

analyze931.0ms (7.8%)

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

sample259.0ms (2.2%)

Algorithm

1×

intervals

Results

83.0ms	118×	body	1280	valid
57.0ms	86×	body	1280	nan
33.0ms	68×	body	640	nan
31.0ms	64×	body	640	valid
17.0ms	45×	body	320	nan
12.0ms	34×	body	320	valid
9.0ms	27×	body	160	valid
2.0ms	13×	body	80	valid
1.0ms	6×	body	160	nan

simplify457.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5009	37

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 60.1b

Counts

2 → 1

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4.0) f)
0.3b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))))
1.5b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))))
6.7b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
36×	`log-prod_binary64`
14×	`add-exp-log_binary64`
13×	`distribute-lft-out_binary64` `cosh-undef_binary64` `associate-l_binary64`
12×	`sinh-undef_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
11×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
5×	`associate-/l*_binary64`
4×	`associate-/r/_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 → 150

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))))
10.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))))
7.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))
7.0ms	(*.f64 (/.f64 PI.f64 4.0) f)

series123.0ms (1%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))))
31.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f)))))
29.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4.0) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4.0) f))))
5.0ms	(*.f64 (/.f64 PI.f64 4.0) f)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4923	4834
1	4923	4834

prune475.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	4	163

Merged error: 2.1b

Counts

163 → 4

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (-.f64 (+.f64 (.f64 0.020833333333333336 (.f64 (.f64 PI.f64 PI.f64) (.f64 f f))) (log.f64 (/.f64 4.0 PI.f64))) (+.f64 (log.f64 f) (+.f64 (.f64 0.0034722222222222225 (/.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) (.f64 4.0 4.0))) (.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) 8.68055555555556e-05)))))
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
2.0b	(log.f64 (/.f64 4.0 PI.f64))

rewrite63.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`
18×	`add-exp-log_binary64`
13×	`log-prod_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
8×	`flip3-+_binary64` `flip-+_binary64` `frac-sub_binary64`
7×	`associate-r_binary64`
6×	`pow-unpow_binary64` `associate-*r/_binary64` `unpow-prod-down_binary64` `frac-times_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64`
3×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `pow-exp_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `log-div_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 144

Calls

4 calls:

49.0ms	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (-.f64 (+.f64 (.f64 0.020833333333333336 (.f64 (.f64 PI.f64 PI.f64) (.f64 f f))) (log.f64 (/.f64 4.0 PI.f64))) (+.f64 (log.f64 f) (+.f64 (.f64 0.0034722222222222225 (/.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) (.f64 4.0 4.0))) (.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) 8.68055555555556e-05)))))
3.0ms	(log.f64 (/.f64 4.0 PI.f64))
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)

series29.0ms (0.2%)

Counts

4 → 6

Calls

4 calls:

29.0ms	(.f64 (/.f64 1.0 (/.f64 PI.f64 4.0)) (-.f64 (+.f64 (.f64 0.020833333333333336 (.f64 (.f64 PI.f64 PI.f64) (.f64 f f))) (log.f64 (/.f64 4.0 PI.f64))) (+.f64 (log.f64 f) (+.f64 (.f64 0.0034722222222222225 (/.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) (.f64 4.0 4.0))) (.f64 (.f64 (pow.f64 PI.f64 4) (pow.f64 f 4)) 8.68055555555556e-05)))))
0.0ms	(log.f64 (/.f64 4.0 PI.f64))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5658	5952

prune578.0ms (4.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	7	150
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	144	10	154

Merged error: 1.8b

Counts

154 → 10

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (log.f64 f) PI.f64)
0.4b	(-.f64 (+.f64 (.f64 4.0 (/.f64 (log.f64 (/.f64 4.0 PI.f64)) PI.f64)) (.f64 0.08333333333333334 (.f64 PI.f64 (.f64 f f)))) (+.f64 (.f64 4.0 (/.f64 (log.f64 f) PI.f64)) (.f64 (pow.f64 PI.f64 3) (*.f64 (pow.f64 f 4) 0.001215277777777778))))
1.0b	(pow.f64 PI.f64 3)
2.0b	(log.f64 (/.f64 4.0 PI.f64))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
16×	`add-log-exp_binary64`
13×	`log-prod_binary64`
10×	`pow1_binary64` `add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`flip3-+_binary64` `diff-log_binary64` `associate-/l*_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
2×	`rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `cube-mult_binary64`

Counts

4 → 100

Calls

4 calls:

19.0ms	(-.f64 (+.f64 (.f64 4.0 (/.f64 (log.f64 (/.f64 4.0 PI.f64)) PI.f64)) (.f64 0.08333333333333334 (.f64 PI.f64 (.f64 f f)))) (+.f64 (.f64 4.0 (/.f64 (log.f64 f) PI.f64)) (.f64 (pow.f64 PI.f64 3) (*.f64 (pow.f64 f 4) 0.001215277777777778))))
4.0ms	(/.f64 (log.f64 f) PI.f64)
3.0ms	(log.f64 (/.f64 4.0 PI.f64))
2.0ms	(pow.f64 PI.f64 3)

series38.0ms (0.3%)

Counts

4 → 8

Calls

4 calls:

26.0ms	(-.f64 (+.f64 (.f64 4.0 (/.f64 (log.f64 (/.f64 4.0 PI.f64)) PI.f64)) (.f64 0.08333333333333334 (.f64 PI.f64 (.f64 f f)))) (+.f64 (.f64 4.0 (/.f64 (log.f64 f) PI.f64)) (.f64 (pow.f64 PI.f64 3) (*.f64 (pow.f64 f 4) 0.001215277777777778))))
12.0ms	(/.f64 (log.f64 f) PI.f64)
0.0ms	(log.f64 (/.f64 4.0 PI.f64))
0.0ms	(pow.f64 PI.f64 3)

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5335	2161

prune250.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	108	10	118

Merged error: 1.8b

Counts

118 → 10

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 (cbrt.f64 PI.f64) 4)
1.6b	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
1.6b	(pow.f64 PI.f64 4)
2.0b	(log.f64 (/.f64 4.0 PI.f64))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13×	`log-prod_binary64`
11×	`add-exp-log_binary64`
9×	`pow-unpow_binary64` `times-frac_binary64`
7×	`pow1_binary64`
6×	`cbrt-prod_binary64` `pow-exp_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64`
2×	`rem-log-exp_binary64`
1×	`unpow2_binary64` `pow1/3_binary64` `log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 89

Calls

4 calls:

7.0ms	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
3.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)
3.0ms	(log.f64 (/.f64 4.0 PI.f64))
3.0ms	(pow.f64 PI.f64 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(log.f64 (/.f64 4.0 PI.f64))
0.0ms	(pow.f64 (pow.f64 (cbrt.f64 PI.f64) 2) 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 (cbrt.f64 PI.f64) 4)

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4914	753
1	4914	753

prune243.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	93	10	103

Merged error: 1.8b

Counts

103 → 10

regimes289.0ms (2.4%)

Accuracy

Total 0.8b remaining (30.8%)

Threshold costs 0.8b (30.8%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	512	33
1	512	33

end0.0ms (0%)

sample7.8s (65.3%)

Algorithm

1×

intervals

Results

2.4s	3435×	body	1280	valid
1.8s	2941×	body	1280	nan
1.2s	2467×	body	640	valid
1.1s	2432×	body	640	nan
450.0ms	1255×	body	320	valid
409.0ms	1207×	body	320	nan
152.0ms	592×	body	160	valid
62.0ms	270×	body	160	nan
33.0ms	251×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze931.0ms (7.8%)

sample259.0ms (2.2%)

simplify457.0ms (3.8%)

prune7.0ms (0.1%)

localize17.0ms (0.1%)

rewrite43.0ms (0.4%)

series123.0ms (1%)

simplify79.0ms (0.7%)

prune475.0ms (4%)

localize29.0ms (0.2%)

rewrite63.0ms (0.5%)

series29.0ms (0.2%)

simplify62.0ms (0.5%)

prune578.0ms (4.8%)

localize24.0ms (0.2%)

rewrite32.0ms (0.3%)

series38.0ms (0.3%)

simplify40.0ms (0.3%)

prune250.0ms (2.1%)

localize38.0ms (0.3%)

rewrite18.0ms (0.1%)

series0.0ms (0%)

simplify40.0ms (0.3%)

prune243.0ms (2%)

regimes289.0ms (2.4%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample7.8s (65.3%)

Profiling