Details

analyze469.0ms (12.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample43.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms	36×	body	2560	valid
8.0ms	163×	body	80	valid
6.0ms	23×	body	1280	valid
4.0ms	21×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	24×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	12×	body	80	invalid
0.0ms	2×	body	160	valid

simplify260.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (258.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune9.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 37.4b

Counts

2 → 1

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
1.4b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64` `associate-/l*_binary64` `times-frac_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`diff-log_binary64` `distribute-rgt-neg-in_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 75

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series72.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
21.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
10.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))

simplify45.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5946	1448

prune147.0ms (3.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	9	88

Merged error: 7.0b

Counts

88 → 9

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
3.1b	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
11.7b	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite46.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
30×	`times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
11×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
4×	`distribute-lft-out--_binary64` `div-inv_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 109

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
13.0ms	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
7.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series161.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
56.0ms	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
10.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5287	2393

prune177.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	122	8	130

Merged error: 6.9b

Counts

130 → 8

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
1.4b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 81

Calls

4 calls:

14.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))

series110.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
11.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune133.0ms (3.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	93	8	101

Merged error: 6.9b

Counts

101 → 8

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (/.f64 1 (*.f64 a 2.0)))
1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
1.4b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
13×	`add-cbrt-cube_binary64`
10×	`add-log-exp_binary64` `prod-exp_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`cbrt-unprod_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
3×	`diff-log_binary64` `times-frac_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `distribute-rgt-neg-in_binary64` `rec-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

17.0ms	(.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (/.f64 1 (*.f64 a 2.0)))
9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series73.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (/.f64 1 (*.f64 a 2.0)))
21.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
10.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5028	1531

prune109.0ms (2.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	95	8	103

Merged error: 6.9b

Counts

103 → 8

regimes385.0ms (10%)

Accuracy

Total 1.3b remaining (18.4%)

Threshold costs 0b (0%)

bsearch89.0ms (2.3%)

Steps

Iters	Range	Point
7	2.1244901091466005e+48	2.2767001911669423e+50	2.2272767242843476e+50
7	3.5591382758316196e-227	5.0477177829490085e-225	1.4168306912023101e-226
9	-3.586326328619297e+155	-1.5727980192684642e+150	-1.277061339333756e+154

Iters

Range

Point

2.1244901091466005e+48

2.2767001911669423e+50

2.2272767242843476e+50

3.5591382758316196e-227

5.0477177829490085e-225

1.4168306912023101e-226

-3.586326328619297e+155

-1.5727980192684642e+150

-1.277061339333756e+154

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	125	61
1	125	61

end0.0ms (0%)

sample1.2s (32%)

Algorithm

1×

intervals

Results

318.0ms	1053×	body	2560	valid
271.0ms	5165×	body	80	valid
224.0ms	926×	body	1280	valid
89.0ms	445×	body	640	valid
43.0ms	119×	body	5120	valid
32.0ms	658×	body	80	nan
31.0ms	198×	body	320	valid
18.0ms	355×	body	80	invalid
9.0ms	94×	body	160	valid

Details

analyze469.0ms (12.1%)

sample43.0ms (1.1%)

simplify260.0ms (6.7%)

prune9.0ms (0.2%)

localize12.0ms (0.3%)

rewrite33.0ms (0.9%)

series72.0ms (1.9%)

simplify45.0ms (1.2%)

prune147.0ms (3.8%)

localize12.0ms (0.3%)

rewrite46.0ms (1.2%)

series161.0ms (4.2%)

simplify41.0ms (1.1%)

prune177.0ms (4.6%)

localize13.0ms (0.3%)

rewrite34.0ms (0.9%)

series110.0ms (2.9%)

simplify68.0ms (1.8%)

prune133.0ms (3.4%)

localize12.0ms (0.3%)

rewrite38.0ms (1%)

series73.0ms (1.9%)

simplify30.0ms (0.8%)

prune109.0ms (2.8%)

regimes385.0ms (10%)

bsearch89.0ms (2.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (32%)

Profiling