Details

analyze1.9s (10.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
3.1%	96.5%	0.3%	9
4.7%	95%	0.3%	10
4.7%	95%	0.3%	11
5.1%	82.1%	12.8%	12
6.2%	74.7%	19%	13
6.4%	74.5%	19%	14

Compiler

Compiled 34 to 30 computations (11.8% saved)

sample70.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
21.0ms	170×	body	128	nan

Compiler

Compiled 67 to 66 computations (1.5% saved)

simplify203.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4980	44
1	4980	44

prune5.0ms (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: 5.0b

Counts

2 → 1

Compiler

Compiled 58 to 50 computations (13.8% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 z (sqrt.f64 (+.f64 t a)))
0.4b	(/.f64 2/3 t)
3.7b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.4b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_13915`
20×	`frac-sub_binary64_13903`
19×	`*-un-lft-identity_binary64_13894`
17×	`add-cube-cbrt_binary64_13926`
13×	`add-exp-log_binary64_13929` `add-cbrt-cube_binary64_13927`
12×	`times-frac_binary64_13900`
9×	`flip3--_binary64_13898` `flip--_binary64_13869`
8×	`frac-times_binary64_13904` `associate-*r/_binary64_13838`
7×	`associate-r_binary64_13836`
6×	`pow1_binary64_13952` `add-log-exp_binary64_13930` `associate-/r*_binary64_13840`
5×	`flip-+_binary64_13868` `sqrt-prod_binary64_13909` `flip3-+_binary64_13897`
4×	`associate-/l*_binary64_13841` `associate--r+_binary64_13832` `sqrt-div_binary64_13910`
3×	`cbrt-undiv_binary64_13925` `div-exp_binary64_13942` `sub-neg_binary64_13887` `associate-l_binary64_13837`
2×	`div-inv_binary64_13891` `associate-*l/_binary64_13839` `associate--l+_binary64_13833` `distribute-lft-in_binary64_13845` `prod-exp_binary64_13940` `associate-/l/_binary64_13843` `frac-2neg_binary64_13905` `cbrt-unprod_binary64_13924` `clear-num_binary64_13893` `unswap-sqr_binary64_13862` `distribute-rgt-in_binary64_13846`
1×	`distribute-lft-out_binary64_13847` `*-commutative_binary64_13827` `pow-prod-down_binary64_13962` `diff-log_binary64_13983`

Counts

4 → 104

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
9.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
4.0ms	(/.f64 2/3 t)

series621.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

365.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
131.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
104.0ms	(*.f64 z (sqrt.f64 (+.f64 t a)))
19.0ms	(/.f64 2/3 t)

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4954	2992
1	4954	2992

prune202.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	3	117

Merged error: 1.0b

Counts

117 → 3

Compiler

Compiled 4666 to 2328 computations (50.1% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2/3 t)
4.4b	(log.f64 (exp.f64 (/.f64 2/3 t)))
5.4b	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
5.5b	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_13894` `add-cube-cbrt_binary64_13926` `add-sqr-sqrt_binary64_13915`
21×	`times-frac_binary64_13900`
14×	`log-pow_binary64_13980`
13×	`exp-prod_binary64_13943`
11×	`add-exp-log_binary64_13929` `add-cbrt-cube_binary64_13927`
8×	`frac-sub_binary64_13903`
7×	`flip3--_binary64_13898` `flip--_binary64_13869`
6×	`add-log-exp_binary64_13930` `associate-/r*_binary64_13840`
5×	`pow1_binary64_13952`
4×	`frac-times_binary64_13904` `associate-r/_binary64_13838` `associate-/l_binary64_13841` `associate--r+_binary64_13832`
3×	`cbrt-undiv_binary64_13925` `div-inv_binary64_13891` `log-prod_binary64_13977` `div-exp_binary64_13942` `sub-neg_binary64_13887`
2×	`associate-*l/_binary64_13839` `associate--l+_binary64_13833` `distribute-lft-in_binary64_13845` `associate-/l/_binary64_13843` `frac-2neg_binary64_13905` `clear-num_binary64_13893` `sqrt-div_binary64_13910` `distribute-rgt-in_binary64_13846`
1×	`rem-log-exp_binary64_13932` `flip-+_binary64_13868` `flip3-+_binary64_13897` `prod-exp_binary64_13940` `cbrt-unprod_binary64_13924` `diff-log_binary64_13983`

Counts

4 → 98

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
9.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
6.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
4.0ms	(/.f64 2/3 t)

series762.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

482.0ms	(-.f64 (/.f64 (.f64 z (sqrt.f64 (+.f64 t a))) t) (.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
134.0ms	(log.f64 (exp.f64 (/.f64 2/3 t)))
122.0ms	(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
25.0ms	(/.f64 2/3 t)

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4968	2291
1	4968	2291

prune181.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	110	3	113

Merged error: 1.0b

Counts

113 → 3

Compiler

Compiled 4313 to 2226 computations (48.4% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.3b	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
4.4b	(.f64 t (-.f64 (.f64 a a) 25/36))
6.5b	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
25.4b	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))

rewrite492.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

1530×	`associate-*r/_binary64_13838`
768×	`frac-sub_binary64_13903`
713×	`flip3--_binary64_13898` `flip--_binary64_13869`
528×	`frac-times_binary64_13904`
360×	`sqrt-div_binary64_13910`
180×	`flip-+_binary64_13868` `flip3-+_binary64_13897`
168×	`associate-*l/_binary64_13839`
162×	`associate-/l/_binary64_13843`
29×	`add-exp-log_binary64_13929` `add-cbrt-cube_binary64_13927`
17×	`sub-neg_binary64_13887`
13×	`add-sqr-sqrt_binary64_13915`
12×	`distribute-lft-in_binary64_13845` `distribute-rgt-in_binary64_13846`
11×	`prod-exp_binary64_13940` `cbrt-unprod_binary64_13924`
10×	`associate--l+_binary64_13833`
8×	`pow1_binary64_13952` `*-un-lft-identity_binary64_13894` `add-cube-cbrt_binary64_13926`
7×	`associate-r_binary64_13836`
6×	`cbrt-undiv_binary64_13925` `div-exp_binary64_13942` `associate--r+_binary64_13832` `add-log-exp_binary64_13930` `associate-l_binary64_13837`
2×	`associate-/r/_binary64_13842` `*-commutative_binary64_13827` `pow-prod-down_binary64_13962` `unswap-sqr_binary64_13862`
1×	`div-inv_binary64_13891` `times-frac_binary64_13900` `associate-/l_binary64_13841` `frac-2neg_binary64_13905` `clear-num_binary64_13893` `associate-/r_binary64_13840` `difference-of-squares_binary64_13863` `diff-log_binary64_13983`

Counts

4 → 577

Calls

4 calls:

71.0ms	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))
59.0ms	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
32.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
9.0ms	(.f64 t (-.f64 (.f64 a a) 25/36))

series3.8s (21.3%)

Counts

4 → 12

Calls

4 calls:

1.6s	(/.f64 (.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))) (.f64 t (*.f64 t (-.f64 a 5/6))))
1.3s	(.f64 t (-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (*.f64 2/3 (-.f64 a 5/6))))))
941.0ms	(-.f64 (.f64 (.f64 z (sqrt.f64 (+.f64 t a))) (-.f64 a 5/6)) (.f64 (-.f64 b c) (-.f64 (.f64 t (-.f64 (.f64 a a) 25/36)) (.f64 2/3 (-.f64 a 5/6)))))
88.0ms	(.f64 t (-.f64 (.f64 a a) 25/36))

simplify490.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

589 → 589

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5348	62096

prune6.0s (33%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	588	1	589
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	588	4	592

Merged error: 1.0b

Counts

592 → 4

Compiler

Compiled 73806 to 38560 computations (47.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 a 5/6)
0.0b	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
0.1b	(*.f64 c (+.f64 a 5/6))
2.2b	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_13894`
11×	`add-sqr-sqrt_binary64_13915`
9×	`add-cube-cbrt_binary64_13926`
8×	`add-log-exp_binary64_13930`
7×	`pow1_binary64_13952`
6×	`add-exp-log_binary64_13929` `add-cbrt-cube_binary64_13927`
4×	`associate--l+_binary64_13833` `pow-pow_binary64_13963` `associate-r_binary64_13836` `unpow-prod-down_binary64_13970`
3×	`distribute-lft-in_binary64_13845` `exp-prod_binary64_13943` `unpow-prod-up_binary64_13969` `associate-l_binary64_13837` `distribute-rgt-in_binary64_13846` `pow-unpow_binary64_13968`
2×	`flip-+_binary64_13868` `sub-neg_binary64_13887` `distribute-lft-out_binary64_13847` `associate-*r/_binary64_13838` `flip3-+_binary64_13897`
1×	`+-commutative_binary64_13826` `flip3--_binary64_13898` `*-commutative_binary64_13827` `pow-prod-down_binary64_13962` `prod-exp_binary64_13940` `flip--_binary64_13869` `cbrt-unprod_binary64_13924` `pow-to-exp_binary64_13960` `exp-lft-sqr_binary64_13946` `unswap-sqr_binary64_13862` `pow-sub_binary64_13967` `sqr-pow_binary64_13866` `sum-log_binary64_13982` `diff-log_binary64_13983` `pow-exp_binary64_13959`

Counts

4 → 73

Calls

4 calls:

14.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
8.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
7.0ms	(*.f64 c (+.f64 a 5/6))
4.0ms	(+.f64 a 5/6)

series234.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(pow.f64 (exp.f64 2) (-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b)))
53.0ms	(-.f64 (.f64 c (+.f64 a 5/6)) (.f64 a b))
42.0ms	(*.f64 c (+.f64 a 5/6))
21.0ms	(+.f64 a 5/6)

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5019	1239

prune98.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	85	4	89

Merged error: 1.0b

Counts

89 → 4

Compiler

Compiled 1944 to 1143 computations (41.2% saved)

regimes194.0ms (1.1%)

Compiler: Compiled 932 to 922 computations (1.1% saved)

bsearch137.0ms (0.8%)

Steps

Iters	Range		Point
9	8.98938904901203e-08	52.871436239658145	0.0009342284343787046
5	-4.7362346873985855e-09	-1.2585438776023698e-09	-1.939682565348763e-09

Compiler

Compiled 1 to 7 computations (-600% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	663	133
1	663	133

end0.0ms (0%)

sample2.1s (11.9%)

Algorithm

1×

intervals

Results

814.0ms	8000×	body	128	valid
497.0ms	5090×	body	128	nan

Compiler

Compiled 357 to 285 computations (20.2% saved)

Details

analyze1.9s (10.7%)

sample70.0ms (0.4%)

simplify203.0ms (1.1%)

prune5.0ms (0%)

localize27.0ms (0.1%)

rewrite51.0ms (0.3%)

series621.0ms (3.4%)

simplify60.0ms (0.3%)

prune202.0ms (1.1%)

localize25.0ms (0.1%)

rewrite48.0ms (0.3%)

series762.0ms (4.2%)

simplify72.0ms (0.4%)

prune181.0ms (1%)

localize32.0ms (0.2%)

rewrite492.0ms (2.7%)

series3.8s (21.3%)

simplify490.0ms (2.7%)

prune6.0s (33%)

localize15.0ms (0.1%)

rewrite39.0ms (0.2%)

series234.0ms (1.3%)

simplify106.0ms (0.6%)

prune98.0ms (0.5%)

regimes194.0ms (1.1%)

bsearch137.0ms (0.8%)

simplify19.0ms (0.1%)

end0.0ms (0%)

sample2.1s (11.9%)

Profiling