Details

analyze468.0ms (7.3%)

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)

sample44.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	43×	body	2048	valid
9.0ms	162×	body	128	valid
7.0ms	24×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	34×	body	128	nan
1.0ms	8×	body	512	valid
1.0ms	7×	body	256	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify415.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (321.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune7.0ms (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: 31.9b

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))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite34.0ms (0.5%)

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:

11.0ms	(/.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series261.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune123.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 4.8b

Counts

87 → 8

Compiler

Compiled 2105 to 1261 computations (40.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite98.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_2812`
439×	`add-sqr-sqrt_binary64_2828`
364×	`*-un-lft-identity_binary64_2806`
290×	`add-cube-cbrt_binary64_2841`
74×	`difference-of-squares_binary64_2775`
71×	`associate-/r*_binary64_2750`
40×	`sqrt-prod_binary64_2822`
37×	`distribute-lft-out--_binary64_2758`
25×	`add-exp-log_binary64_2844`
17×	`div-inv_binary64_2803`
15×	`div-exp_binary64_2857`
13×	`add-cbrt-cube_binary64_2842`
8×	`add-log-exp_binary64_2845`
6×	`cbrt-undiv_binary64_2840` `pow1_binary64_2867`
5×	`associate-/r/_binary64_2752`
4×	`cancel-sign-sub-inv_binary64_2772`
3×	`1-exp_binary64_2850` `rec-exp_binary64_2856` `flip3--_binary64_2810` `flip--_binary64_2781` `associate-/l*_binary64_2751`
2×	`sqrt-div_binary64_2823` `diff-log_binary64_2898` `sub-neg_binary64_2799`
1×	`pow1/2_binary64_2886` `pow-flip_binary64_2880` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `inv-pow_binary64_2891` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 356

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series302.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
71.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify189.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4968	16295
1	4968	16295

prune769.0ms (11.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	366	2	368
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	367	9	376

Merged error: 4.7b

Counts

376 → 9

Compiler

Compiled 12744 to 7701 computations (39.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
21.0b	(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)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series278.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
67.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5360	2202

prune105.0ms (1.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Merged error: 4.7b

Counts

104 → 9

Compiler

Compiled 2298 to 1382 computations (39.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_2828` `add-log-exp_binary64_2845`
6×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `sqrt-prod_binary64_2822` `pow1_binary64_2867`
4×	`sqrt-div_binary64_2823` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `flip3--_binary64_2810` `flip--_binary64_2781`
2×	`pow1/2_binary64_2886` `cancel-sign-sub-inv_binary64_2772` `sqrt-pow1_binary64_2824` `diff-log_binary64_2898` `sub-neg_binary64_2799` `rem-sqrt-square_binary64_2819`

Counts

4 → 54

Calls

4 calls:

4.0ms	(-.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)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series185.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4949	1236
1	4949	1236

prune99.0ms (1.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	66	9	75

Merged error: 4.7b

Counts

75 → 9

Compiler

Compiled 2448 to 1457 computations (40.5% saved)

regimes647.0ms (10.1%)

Compiler: Compiled 3408 to 2664 computations (21.8% saved)

bsearch94.0ms (1.5%)

Steps

Iters	Range	Point
6	4.251331648447405e+36	2.988953343593775e+37	2.382809818126237e+37
9	2.3495110806852173e-299	3.6907232803257034e-294	2.595266346017017e-294
9	-1.8958728708534682e+158	-1.060642277646745e+153	-2.302834620394509e+153

Iters

Range

Point

4.251331648447405e+36

2.988953343593775e+37

2.382809818126237e+37

2.3495110806852173e-299

3.6907232803257034e-294

2.595266346017017e-294

-1.8958728708534682e+158

-1.060642277646745e+153

-2.302834620394509e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	113	97
1	113	97

end0.0ms (0%)

sample2.0s (30.7%)

Algorithm

1×

intervals

Results

285.0ms	5229×	body	128	valid
285.0ms	1075×	body	2048	valid
150.0ms	749×	body	1024	valid
124.0ms	395×	body	4096	valid
55.0ms	359×	body	512	valid
35.0ms	696×	body	128	nan
22.0ms	423×	body	128	invalid
19.0ms	193×	body	256	valid

Compiler

Compiled 912 to 703 computations (22.9% saved)

Details

analyze468.0ms (7.3%)

sample44.0ms (0.7%)

simplify415.0ms (6.5%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

rewrite34.0ms (0.5%)

series261.0ms (4.1%)

simplify93.0ms (1.5%)

prune123.0ms (1.9%)

localize12.0ms (0.2%)

rewrite98.0ms (1.5%)

series302.0ms (4.7%)

simplify189.0ms (2.9%)

prune769.0ms (11.9%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series278.0ms (4.3%)

simplify78.0ms (1.2%)

prune105.0ms (1.6%)

localize13.0ms (0.2%)

rewrite25.0ms (0.4%)

series185.0ms (2.9%)

simplify58.0ms (0.9%)

prune99.0ms (1.5%)

regimes647.0ms (10.1%)

bsearch94.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (30.7%)

Profiling