Details

analyze1.8s (0.3%)

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)

sample222.0ms (0%)

Algorithm

1×

intervals

Results

77.0ms	45×	body	2048	valid
35.0ms	25×	body	1024	valid
31.0ms	149×	body	128	valid
28.0ms	16×	body	4096	valid
12.0ms	14×	body	512	valid
3.0ms	25×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify860.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (659.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune10.0ms (0%)

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: 37.2b

Counts

2 → 2

Compiler

Compiled 49 to 40 computations (18.4% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite105.0ms (0%)

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-/l*_binary64_2751`
3×	`associate-/r*_binary64_2750` `sqrt-prod_binary64_2822`
2×	`sqrt-div_binary64_2823` `associate-/l/_binary64_2753` `flip3--_binary64_2810` `flip-+_binary64_2780` `flip--_binary64_2781` `flip3-+_binary64_2809`
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:

39.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
18.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series652.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
196.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
147.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
73.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify197.0ms (0%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune1.3s (0.2%)

Pruning

49 alts after pruning (48 fresh and 1 done)

	Pruned	Kept	Total
New	37	47	84
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	37	49	86

Merged error: 6.6b

Counts

86 → 49

Compiler

Compiled 3336 to 1984 computations (40.5% saved)

localize56.0ms (0%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.8b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.5b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite223.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_2812`
59×	`add-sqr-sqrt_binary64_2828`
44×	`*-un-lft-identity_binary64_2806`
30×	`add-cube-cbrt_binary64_2841`
27×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
14×	`difference-of-squares_binary64_2775`
13×	`sqrt-prod_binary64_2822` `associate-/l*_binary64_2751`
10×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `associate-/r/_binary64_2752`
9×	`associate-/r*_binary64_2750`
7×	`flip3--_binary64_2810` `distribute-lft-out--_binary64_2758` `flip--_binary64_2781`
6×	`cancel-sign-sub-inv_binary64_2772` `div-inv_binary64_2803` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `add-log-exp_binary64_2845`
5×	`pow1_binary64_2867`
2×	`sqrt-div_binary64_2823` `clear-num_binary64_2805` `frac-2neg_binary64_2817`
1×	`associate-/l/_binary64_2753` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `diff-log_binary64_2898` `sub-neg_binary64_2799` `rem-sqrt-square_binary64_2819`

Counts

4 → 136

Calls

4 calls:

59.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
49.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
32.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series2.1s (0.3%)

Counts

4 → 12

Calls

4 calls:

804.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
659.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
324.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
269.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify517.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (317.0ms)

Iter	Nodes	Cost
0	5011	5032

prune5.0s (0.8%)

Pruning

123 alts after pruning (122 fresh and 1 done)

	Pruned	Kept	Total
New	73	75	148
Fresh	0	47	47
Picked	1	0	1
Done	0	1	1
Total	74	123	197

Merged error: 6.5b

Counts

197 → 123

Compiler

Compiled 8760 to 5200 computations (40.6% saved)

localize58.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite140.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_2828`
28×	`*-un-lft-identity_binary64_2806`
18×	`times-frac_binary64_2812` `add-cube-cbrt_binary64_2841`
11×	`sqrt-prod_binary64_2822`
10×	`difference-of-squares_binary64_2775`
8×	`add-log-exp_binary64_2845`
7×	`cancel-sign-sub-inv_binary64_2772`
6×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `associate-/r*_binary64_2750`
5×	`distribute-lft-out--_binary64_2758` `pow1_binary64_2867`
4×	`flip3--_binary64_2810` `flip--_binary64_2781`
3×	`associate-/l*_binary64_2751`
2×	`sqrt-div_binary64_2823` `diff-log_binary64_2898` `sub-neg_binary64_2799` `associate-/r/_binary64_2752`
1×	`pow1/2_binary64_2886` `div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 88

Calls

4 calls:

37.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
31.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
19.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series1.3s (0.2%)

Counts

4 → 12

Calls

4 calls:

600.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
277.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
242.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
146.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify353.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (263.0ms)

Iter	Nodes	Cost
0	4882	2580
1	4882	2580

prune4.9s (0.8%)

Pruning

165 alts after pruning (163 fresh and 2 done)

	Pruned	Kept	Total
New	52	48	100
Fresh	6	115	121
Picked	0	1	1
Done	0	1	1
Total	58	165	223

Merged error: 6.5b

Counts

223 → 165

Compiler

Compiled 8563 to 5694 computations (33.5% saved)

localize80.0ms (0%)

Local error

Found 4 expressions with local error:

23.8b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite292.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-div_binary64_2838`
30×	`flip3--_binary64_2810` `flip--_binary64_2781`
28×	`frac-times_binary64_2816`
26×	`sqrt-div_binary64_2823`
24×	`pow1_binary64_2867`
15×	`sqrt-pow1_binary64_2824`
14×	`associate-*l/_binary64_2749`
12×	`pow1/3_binary64_2888`
9×	`pow-prod-up_binary64_2876` `cbrt-prod_binary64_2837`
8×	`associate-*r/_binary64_2748`
7×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
6×	`pow-plus_binary64_2869`
5×	`pow-prod-down_binary64_2877`
4×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-log-exp_binary64_2845`
3×	`pow-sqr_binary64_2779`
2×	`pow2_binary64_2887`
1×	`pow1/2_binary64_2886` `pow3_binary64_2889` `sqrt-prod_binary64_2822`

Counts

4 → 89

Calls

4 calls:

116.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
26.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
19.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
18.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series1.4s (0.2%)

Counts

4 → 12

Calls

4 calls:

475.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
448.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
290.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
197.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify357.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (185.0ms)

Iter	Nodes	Cost
0	5019	3801

prune4.2s (0.7%)

Pruning

195 alts after pruning (192 fresh and 3 done)

	Pruned	Kept	Total
New	70	31	101
Fresh	1	161	162
Picked	0	1	1
Done	0	2	2
Total	71	195	266

Merged error: 6.5b

Counts

266 → 195

Compiler

Compiled 5322 to 3173 computations (40.4% saved)

regimes20.8s (3.5%)

Compiler: Compiled 42526 to 29902 computations (29.7% saved)

bsearch9.2min (92.2%)

Steps

Iters	Range		Point
7	5.793216464298443e+95	3.638953618106178e+97	4.491843677964469e+96
9	2.0439136282214333e-216	7.118422179303289e-211	5.342886467585216e-215
10	-5.167850974433525e+99	-4.63632807356662e+86	-7.019421680264921e+98

Compiler

Compiled 1 to 3 computations (-200% saved)

Details

analyze1.8s (0.3%)

sample222.0ms (0%)

simplify860.0ms (0.1%)

prune10.0ms (0%)

localize21.0ms (0%)

rewrite105.0ms (0%)

series652.0ms (0.1%)

simplify197.0ms (0%)

prune1.3s (0.2%)

localize56.0ms (0%)

rewrite223.0ms (0%)

series2.1s (0.3%)

simplify517.0ms (0.1%)

prune5.0s (0.8%)

localize58.0ms (0%)

rewrite140.0ms (0%)

series1.3s (0.2%)

simplify353.0ms (0.1%)

prune4.9s (0.8%)

localize80.0ms (0%)

rewrite292.0ms (0%)

series1.4s (0.2%)

simplify357.0ms (0.1%)

prune4.2s (0.7%)

regimes20.8s (3.5%)

bsearch9.2min (92.2%)

Profiling