Details

analyze477.0ms (8.2%)

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)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	175×	body	128	valid
8.0ms	29×	body	2048	valid
5.0ms	25×	body	1024	valid
5.0ms	14×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	23×	body	128	nan
1.0ms	13×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify411.0ms (7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (318.0ms)

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

Merged error: 33.3b

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))
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
22.4b	(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:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.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))

series263.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify89.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune125.0ms (2.1%)

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: 5.6b

Counts

87 → 8

Compiler

Compiled 2145 to 1281 computations (40.3% 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))
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite42.0ms (0.7%)

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:

18.0ms	(.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)))

series276.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5360	2202

prune105.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Merged error: 5.6b

Counts

103 → 7

Compiler

Compiled 2294 to 1372 computations (40.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.6b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
15.4b	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
14×	`*-un-lft-identity_binary64_2806` `pow1_binary64_2867`
13×	`add-sqr-sqrt_binary64_2828` `associate-r_binary64_2746`
12×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `add-cube-cbrt_binary64_2841`
9×	`times-frac_binary64_2812`
8×	`add-log-exp_binary64_2845`
6×	`pow-prod-down_binary64_2877`
3×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sqrt-prod_binary64_2822`
2×	`sqrt-div_binary64_2823` `flip3--_binary64_2810` `flip--_binary64_2781`
1×	`associate-l_binary64_2747` `pow1/2_binary64_2886` `cancel-sign-sub-inv_binary64_2772` `div-inv_binary64_2803` `distribute-lft-out_binary64_2757` `-commutative_binary64_2737` `sqrt-pow1_binary64_2824` `diff-log_binary64_2898` `sub-neg_binary64_2799` `rem-sqrt-square_binary64_2819` `flip-+_binary64_2780` `sum-log_binary64_2897` `flip3-+_binary64_2809` `associate-r/_binary64_2748` `+-commutative_binary64_2736`

Counts

4 → 77

Calls

4 calls:

10.0ms	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))
7.0ms	(+.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)))

series166.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
10.0ms	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4936	1466
1	4936	1466

prune107.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 5.5b

Counts

96 → 8

Compiler

Compiled 2446 to 1474 computations (39.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.6b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_2806`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
8×	`add-sqr-sqrt_binary64_2828` `add-log-exp_binary64_2845`
7×	`add-cube-cbrt_binary64_2841`
5×	`pow1_binary64_2867`
4×	`times-frac_binary64_2812` `associate-/r*_binary64_2750`
3×	`distribute-lft-out_binary64_2757` `sqrt-prod_binary64_2822`
2×	`sqrt-div_binary64_2823` `div-exp_binary64_2857` `flip3--_binary64_2810` `cbrt-undiv_binary64_2840` `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` `sqrt-pow1_binary64_2824` `diff-log_binary64_2898` `prod-exp_binary64_2855` `sub-neg_binary64_2799` `cbrt-unprod_binary64_2839` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `clear-num_binary64_2805` `associate-/l*_binary64_2751` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

4 → 64

Calls

4 calls:

10.0ms	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
7.0ms	(+.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))

series341.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
63.0ms	(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))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4951	1690
1	4951	1690

prune79.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	76	8	84

Merged error: 5.5b

Counts

84 → 8

Compiler

Compiled 1710 to 1005 computations (41.2% saved)

regimes682.0ms (11.7%)

Compiler: Compiled 4224 to 3216 computations (23.9% saved)

bsearch107.0ms (1.8%)

Steps

Iters	Range	Point
7	7.482650775739311e+127	6.940404749714049e+129	1.928533493233392e+129
9	4.1267928365631376e-194	6.602297926380012e-187	4.190818973144896e-194
7	-3.1670677211042097e+132	-3.885194447819339e+130	-3.475153330017618e+131

Iters

Range

Point

7.482650775739311e+127

6.940404749714049e+129

1.928533493233392e+129

4.1267928365631376e-194

6.602297926380012e-187

4.190818973144896e-194

-3.1670677211042097e+132

-3.885194447819339e+130

-3.475153330017618e+131

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	102	82
1	102	82

end0.0ms (0%)

sample2.1s (36.8%)

Algorithm

1×

intervals

Results

315.0ms	1171×	body	2048	valid
296.0ms	5164×	body	128	valid
151.0ms	702×	body	1024	valid
132.0ms	394×	body	4096	valid
60.0ms	385×	body	512	valid
38.0ms	703×	body	128	nan
27.0ms	380×	body	128	invalid
20.0ms	184×	body	256	valid

Compiler

Compiled 1106 to 834 computations (24.6% saved)

Details

analyze477.0ms (8.2%)

sample41.0ms (0.7%)

simplify411.0ms (7%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite34.0ms (0.6%)

series263.0ms (4.5%)

simplify89.0ms (1.5%)

prune125.0ms (2.1%)

localize11.0ms (0.2%)

rewrite42.0ms (0.7%)

series276.0ms (4.7%)

simplify83.0ms (1.4%)

prune105.0ms (1.8%)

localize17.0ms (0.3%)

rewrite33.0ms (0.6%)

series166.0ms (2.8%)

simplify63.0ms (1.1%)

prune107.0ms (1.8%)

localize11.0ms (0.2%)

rewrite30.0ms (0.5%)

series341.0ms (5.8%)

simplify80.0ms (1.4%)

prune79.0ms (1.3%)

regimes682.0ms (11.7%)

bsearch107.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (36.8%)

Profiling