Details

analyze861.0ms (8.6%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample74.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	37×	body	2048	valid
16.0ms	169×	body	128	valid
8.0ms	22×	body	1024	valid
7.0ms	12×	body	4096	valid
3.0ms	34×	body	128	nan
3.0ms	10×	body	512	valid
1.0ms	6×	body	256	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify670.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (520.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	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: 30.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
18.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite75.0ms (0.8%)

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:

24.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
13.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series457.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
107.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
98.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify155.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4893	1983
1	4893	1983

prune249.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	11	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	11	87

Merged error: 4.5b

Counts

87 → 11

Compiler

Compiled 2189 to 1324 computations (39.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
18.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite55.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2828`
10×	`pow1_binary64_2867`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `*-un-lft-identity_binary64_2806`
8×	`add-log-exp_binary64_2845`
7×	`add-cube-cbrt_binary64_2841`
4×	`cancel-sign-sub-inv_binary64_2772` `sqrt-prod_binary64_2822`
3×	`flip3--_binary64_2810` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `flip--_binary64_2781` `associate-r_binary64_2746` `pow-prod-down_binary64_2877`
2×	`sqrt-div_binary64_2823` `diff-log_binary64_2898` `sub-neg_binary64_2799` `difference-of-squares_binary64_2775`
1×	`associate-l_binary64_2747` `pow1/2_binary64_2886` `*-commutative_binary64_2737` `sqrt-pow1_binary64_2824` `distribute-lft-out--_binary64_2758` `rem-sqrt-square_binary64_2819`

Counts

4 → 62

Calls

4 calls:

16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
11.0ms	(.f64 (.f64 3 a) c)
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series297.0ms (3%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
97.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
56.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
25.0ms	(.f64 (.f64 3 a) c)

simplify113.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune141.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	74	11	85

Merged error: 4.5b

Counts

85 → 11

Compiler

Compiled 1764 to 1077 computations (38.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3)))) b) (.f64 3 a))
1.2b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
1.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
18.4b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

rewrite69.0ms (0.7%)

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`
3×	`cancel-sign-sub-inv_binary64_2772` `distribute-lft-out--_binary64_2758`
2×	`sqrt-div_binary64_2823` `associate-/l/_binary64_2753` `div-exp_binary64_2857` `flip3--_binary64_2810` `cbrt-undiv_binary64_2840` `flip-+_binary64_2780` `flip--_binary64_2781` `flip3-+_binary64_2809`
1×	`pow1/2_binary64_2886` `div-inv_binary64_2803` `associate-/r*_binary64_2750` `sqrt-pow1_binary64_2824` `div-sub_binary64_2811` `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` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

4 → 73

Calls

4 calls:

23.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3)))) b) (.f64 3 a))
16.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
9.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
9.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

series514.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3)))) b) (.f64 3 a))
123.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))
116.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
65.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4994	1969
1	4994	1969

prune172.0ms (1.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	85	11	96

Merged error: 4.5b

Counts

96 → 11

Compiler

Compiled 2141 to 1293 computations (39.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
18.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite54.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2828`
10×	`pow1_binary64_2867`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `*-un-lft-identity_binary64_2806`
8×	`add-log-exp_binary64_2845`
7×	`add-cube-cbrt_binary64_2841`
4×	`cancel-sign-sub-inv_binary64_2772` `sqrt-prod_binary64_2822`
3×	`flip3--_binary64_2810` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `flip--_binary64_2781` `associate-r_binary64_2746` `pow-prod-down_binary64_2877`
2×	`sqrt-div_binary64_2823` `diff-log_binary64_2898` `sub-neg_binary64_2799` `difference-of-squares_binary64_2775`
1×	`associate-l_binary64_2747` `pow1/2_binary64_2886` `*-commutative_binary64_2737` `sqrt-pow1_binary64_2824` `distribute-lft-out--_binary64_2758` `rem-sqrt-square_binary64_2819`

Counts

4 → 62

Calls

4 calls:

16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
11.0ms	(.f64 (.f64 3 a) c)
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series314.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
110.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
27.0ms	(.f64 (.f64 3 a) c)

simplify121.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune138.0ms (1.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	73	12	85

Merged error: 4.5b

Counts

85 → 12

Compiler

Compiled 1717 to 1073 computations (37.5% saved)

regimes1.5s (14.9%)

Compiler: Compiled 4721 to 3646 computations (22.8% saved)

bsearch105.0ms (1.1%)

Steps

Iters	Range		Point
7	1.5905821695811115e-50	2.0896905838181703e-48	7.334233368061974e-50
8	-2.0922019410616626e+112	-1.82358309996822e+109	-3.1102062341024787e+111

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	109	59
1	109	59

end0.0ms (0%)

sample3.6s (36.5%)

Algorithm

1×

intervals

Results

523.0ms	1087×	body	2048	valid
518.0ms	5243×	body	128	valid
271.0ms	721×	body	1024	valid
238.0ms	396×	body	4096	valid
102.0ms	370×	body	512	valid
72.0ms	695×	body	128	nan
41.0ms	423×	body	128	invalid
34.0ms	183×	body	256	valid

Compiler

Compiled 901 to 693 computations (23.1% saved)

Details

analyze861.0ms (8.6%)

sample74.0ms (0.7%)

simplify670.0ms (6.7%)

prune7.0ms (0.1%)

localize25.0ms (0.3%)

rewrite75.0ms (0.8%)

series457.0ms (4.6%)

simplify155.0ms (1.6%)

prune249.0ms (2.5%)

localize23.0ms (0.2%)

rewrite55.0ms (0.5%)

series297.0ms (3%)

simplify113.0ms (1.1%)

prune141.0ms (1.4%)

localize23.0ms (0.2%)

rewrite69.0ms (0.7%)

series514.0ms (5.2%)

simplify98.0ms (1%)

prune172.0ms (1.7%)

localize23.0ms (0.2%)

rewrite54.0ms (0.5%)

series314.0ms (3.2%)

simplify121.0ms (1.2%)

prune138.0ms (1.4%)

regimes1.5s (14.9%)

bsearch105.0ms (1.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.6s (36.5%)

Profiling