Details

analyze469.0ms (8%)

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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	161×	body	128	valid
8.0ms	33×	body	2048	valid
5.0ms	26×	body	1024	valid
4.0ms	14×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	10×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify405.0ms (6.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (307.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

Error

34.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2828`
14×	`*-un-lft-identity_binary64_2806`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
8×	`add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841`
6×	`times-frac_binary64_2812` `sqrt-prod_binary64_2822` `difference-of-squares_binary64_2775` `associate-/l*_binary64_2751`
5×	`pow1_binary64_2867`
4×	`cancel-sign-sub-inv_binary64_2772` `flip3--_binary64_2810` `flip--_binary64_2781`
3×	`distribute-lft-out--_binary64_2758`
2×	`sqrt-div_binary64_2823` `associate-/l/_binary64_2753` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `diff-log_binary64_2898` `sub-neg_binary64_2799`
1×	`pow1/2_binary64_2886` `div-inv_binary64_2803` `associate-/r*_binary64_2750` `sqrt-pow1_binary64_2824` `div-sub_binary64_2811` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `rem-sqrt-square_binary64_2819` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series266.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
67.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune114.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Error

4.3b

Counts

87 → 7

Compiler

Compiled 2086 to 1245 computations (40.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
8.0b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
22×	`times-frac_binary64_2812`
21×	`*-un-lft-identity_binary64_2806`
17×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
13×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
12×	`add-sqr-sqrt_binary64_2828`
11×	`add-cube-cbrt_binary64_2841` `associate-/l*_binary64_2751`
6×	`add-log-exp_binary64_2845` `associate-/r/_binary64_2752`
5×	`distribute-lft-out_binary64_2757` `associate-/r*_binary64_2750` `pow1_binary64_2867`
4×	`div-inv_binary64_2803` `flip-+_binary64_2780` `flip3-+_binary64_2809`
3×	`sqrt-prod_binary64_2822`
2×	`sqrt-div_binary64_2823` `clear-num_binary64_2805` `frac-2neg_binary64_2817`
1×	`associate-/l/_binary64_2753` `pow1/2_binary64_2886` `flip3--_binary64_2810` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `flip--_binary64_2781` `+-commutative_binary64_2736`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
15.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series497.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
159.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4956	3121
1	4956	3121

prune147.0ms (2.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	114	7	121

Error

4.2b

Counts

121 → 7

Compiler

Compiled 3228 to 1983 computations (38.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2806`
15×	`add-sqr-sqrt_binary64_2828`
14×	`add-cube-cbrt_binary64_2841`
12×	`times-frac_binary64_2812`
8×	`add-log-exp_binary64_2845`
6×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
5×	`distribute-lft-out_binary64_2757` `pow1_binary64_2867`
4×	`associate-/r*_binary64_2750`
3×	`sqrt-prod_binary64_2822` `associate-/l*_binary64_2751`
2×	`sqrt-div_binary64_2823` `flip3--_binary64_2810` `flip-+_binary64_2780` `flip--_binary64_2781` `flip3-+_binary64_2809` `associate-/r/_binary64_2752`
1×	`pow1/2_binary64_2886` `cancel-sign-sub-inv_binary64_2772` `div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `diff-log_binary64_2898` `sub-neg_binary64_2799` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `clear-num_binary64_2805` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series321.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4891	1972
1	4891	1972

prune98.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Error

4.2b

Counts

91 → 7

Compiler

Compiled 2226 to 1380 computations (38% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_2828`
18×	`*-un-lft-identity_binary64_2806`
14×	`add-cube-cbrt_binary64_2841`
13×	`associate-r_binary64_2746`
10×	`times-frac_binary64_2812`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
8×	`add-log-exp_binary64_2845`
7×	`pow1_binary64_2867`
6×	`associate-l_binary64_2747`
5×	`flip3--_binary64_2810` `flip--_binary64_2781` `sqrt-prod_binary64_2822`
4×	`cancel-sign-sub-inv_binary64_2772` `difference-of-squares_binary64_2775`
2×	`frac-times_binary64_2816` `sqrt-div_binary64_2823` `distribute-lft-out--_binary64_2758` `diff-log_binary64_2898` `prod-exp_binary64_2855` `sub-neg_binary64_2799` `cbrt-unprod_binary64_2839` `associate-*l/_binary64_2749` `unswap-sqr_binary64_2774`
1×	`pow1/2_binary64_2886` `div-inv_binary64_2803` `div-exp_binary64_2857` `-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `associate-r/_binary64_2748` `pow-prod-down_binary64_2877`

Counts

4 → 83

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series272.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5360	2202

prune97.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Error

4.2b

Counts

102 → 7

Compiler

Compiled 2191 to 1291 computations (41.1% saved)

regimes518.0ms (8.8%)

Accuracy

Total 1.0b remaining (14.8%)

Threshold costs 1.0b (14.8%)

Compiler

Compiled 3136 to 2504 computations (20.2% saved)

bsearch105.0ms (1.8%)

Steps

Iters	Range	Point
7	1.8515760575460165e+108	7.079746839452132e+109	9.806096002062306e+108
9	3.471655958753961e-308	1.338164201957951e-301	7.151073671652035e-308
9	-3.203657050301464e+105	-6.409993448757428e+99	-3.161255245507665e+105

Iters

Range

Point

1.8515760575460165e+108

7.079746839452132e+109

9.806096002062306e+108

3.471655958753961e-308

1.338164201957951e-301

7.151073671652035e-308

-3.203657050301464e+105

-6.409993448757428e+99

-3.161255245507665e+105

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample1.9s (33.3%)

Algorithm

1×

intervals

Results

282.0ms	5228×	body	128	valid
276.0ms	1110×	body	2048	valid
144.0ms	748×	body	1024	valid
119.0ms	390×	body	4096	valid
52.0ms	332×	body	512	valid
32.0ms	639×	body	128	nan
21.0ms	192×	body	256	valid
19.0ms	359×	body	128	invalid

Compiler

Compiled 834 to 656 computations (21.3% saved)

Details

analyze469.0ms (8%)

sample39.0ms (0.7%)

simplify405.0ms (6.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite34.0ms (0.6%)

series266.0ms (4.5%)

simplify91.0ms (1.6%)

prune114.0ms (1.9%)

localize14.0ms (0.2%)

rewrite51.0ms (0.9%)

series497.0ms (8.5%)

simplify98.0ms (1.7%)

prune147.0ms (2.5%)

localize12.0ms (0.2%)

rewrite28.0ms (0.5%)

series321.0ms (5.5%)

simplify77.0ms (1.3%)

prune98.0ms (1.7%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series272.0ms (4.6%)

simplify83.0ms (1.4%)

prune97.0ms (1.7%)

regimes518.0ms (8.8%)

bsearch105.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (33.3%)

Profiling