Details

analyze711.0ms (9.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4937	96
1	4937	96
0	3	3
1	3	3

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)

sample42.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	44×	body	2048	valid
8.0ms	155×	body	128	valid
6.0ms	30×	body	1024	valid
3.0ms	10×	body	4096	valid
1.0ms	8×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	9×	body	256	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify280.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (275.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	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: 33.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_5556`
10×	`pow1_binary64_5595`
9×	`*-un-lft-identity_binary64_5534` `add-cbrt-cube_binary64_5570` `add-exp-log_binary64_5572`
8×	`add-log-exp_binary64_5573`
7×	`add-cube-cbrt_binary64_5569`
4×	`sqrt-prod_binary64_5550` `cancel-sign-sub-inv_binary64_5500`
3×	`cbrt-unprod_binary64_5567` `flip--_binary64_5509` `associate-r_binary64_5474` `flip3--_binary64_5538` `prod-exp_binary64_5583` `pow-prod-down_binary64_5605`
2×	`sqrt-div_binary64_5551` `diff-log_binary64_5626` `difference-of-squares_binary64_5503` `sub-neg_binary64_5527`
1×	`associate-l_binary64_5475` `distribute-lft-out--_binary64_5486` `*-commutative_binary64_5465` `sqrt-pow1_binary64_5552` `rem-sqrt-square_binary64_5547` `pow1/2_binary64_5614`

Counts

4 → 62

Calls

4 calls:

9.0ms	(.f64 (.f64 3 a) c)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series176.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(.f64 (.f64 3 a) c)

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune104.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	65	9	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	10	75

Merged error: 12.0b

Counts

75 → 10

Compiler

Compiled 1810 to 1101 computations (39.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.1b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
9.4b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_5570` `add-exp-log_binary64_5572`
22×	`times-frac_binary64_5540`
21×	`*-un-lft-identity_binary64_5534`
17×	`div-exp_binary64_5585` `cbrt-undiv_binary64_5568`
13×	`cbrt-unprod_binary64_5567` `prod-exp_binary64_5583`
12×	`add-sqr-sqrt_binary64_5556`
11×	`associate-/l*_binary64_5479` `add-cube-cbrt_binary64_5569`
6×	`add-log-exp_binary64_5573` `associate-/r/_binary64_5480`
5×	`associate-/r*_binary64_5478` `distribute-lft-out_binary64_5485` `pow1_binary64_5595`
4×	`div-inv_binary64_5531` `flip-+_binary64_5508` `flip3-+_binary64_5537`
3×	`sqrt-prod_binary64_5550`
2×	`sqrt-div_binary64_5551` `frac-2neg_binary64_5545` `clear-num_binary64_5533`
1×	`associate-/l/_binary64_5481` `+-commutative_binary64_5464` `sum-log_binary64_5625` `flip--_binary64_5509` `sqrt-pow1_binary64_5552` `rem-sqrt-square_binary64_5547` `pow1/2_binary64_5614` `flip3--_binary64_5538`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series474.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
146.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
58.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4961	3218
1	4961	3218

prune181.0ms (2.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	104	10	114
Fresh	1	7	8
Picked	1	0	1
Done	1	0	1
Total	107	17	124

Merged error: 8.5b

Counts

124 → 17

Compiler

Compiled 3632 to 2274 computations (37.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_5572`
13×	`add-cbrt-cube_binary64_5570`
9×	`*-un-lft-identity_binary64_5534` `div-exp_binary64_5585`
8×	`add-log-exp_binary64_5573` `add-sqr-sqrt_binary64_5556` `pow1_binary64_5595`
7×	`add-cube-cbrt_binary64_5569`
6×	`prod-exp_binary64_5583`
5×	`associate-/r/_binary64_5480`
4×	`cbrt-undiv_binary64_5568`
3×	`sqrt-prod_binary64_5550` `flip-+_binary64_5508` `flip3-+_binary64_5537` `rec-exp_binary64_5584` `times-frac_binary64_5540` `1-exp_binary64_5578` `associate-/l*_binary64_5479`
2×	`associate-*l/_binary64_5477` `sqrt-div_binary64_5551` `cbrt-unprod_binary64_5567` `pow-flip_binary64_5608` `flip--_binary64_5509` `frac-times_binary64_5544` `flip3--_binary64_5538`
1×	`div-inv_binary64_5531` `associate-r/_binary64_5476` `diff-log_binary64_5626` `cancel-sign-sub-inv_binary64_5500` `inv-pow_binary64_5619` `+-commutative_binary64_5464` `sum-log_binary64_5625` `frac-2neg_binary64_5545` `sqrt-pow1_binary64_5552` `associate-/r_binary64_5478` `clear-num_binary64_5533` `rem-sqrt-square_binary64_5547` `distribute-lft-out_binary64_5485` `pow1/2_binary64_5614` `sub-neg_binary64_5527` `pow-prod-down_binary64_5605`

Counts

4 → 76

Calls

4 calls:

13.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series295.0ms (4%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 -1 c)))
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
57.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4940	1859
1	4940	1859

prune116.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	10	6	16
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 4.3b

Counts

105 → 11

Compiler

Compiled 2258 to 1412 computations (37.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
21.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_5595`
9×	`add-cbrt-cube_binary64_5570` `add-exp-log_binary64_5572`
8×	`*-un-lft-identity_binary64_5534` `add-log-exp_binary64_5573`
7×	`add-sqr-sqrt_binary64_5556`
6×	`add-cube-cbrt_binary64_5569`
3×	`sqrt-prod_binary64_5550` `cbrt-unprod_binary64_5567` `associate-r_binary64_5474` `prod-exp_binary64_5583` `pow-prod-down_binary64_5605`
2×	`sqrt-div_binary64_5551` `flip--_binary64_5509` `flip3--_binary64_5538`
1×	`flip-+_binary64_5508` `diff-log_binary64_5626` `cancel-sign-sub-inv_binary64_5500` `associate-l_binary64_5475` `flip3-+_binary64_5537` `+-commutative_binary64_5464` `sum-log_binary64_5625` `*-commutative_binary64_5465` `sqrt-pow1_binary64_5552` `rem-sqrt-square_binary64_5547` `distribute-lft-out_binary64_5485` `pow1/2_binary64_5614` `sub-neg_binary64_5527`

Counts

4 → 57

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series167.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
14.0ms	(.f64 (.f64 3 a) c)

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5147	1126

prune68.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	69	11	80

Merged error: 4.3b

Counts

80 → 11

Compiler

Compiled 1520 to 929 computations (38.9% saved)

regimes1.5s (20%)

Compiler: Compiled 9128 to 6922 computations (24.2% saved)

bsearch111.0ms (1.5%)

Steps

Iters	Range	Point
6	3.1120206868224175e+122	4.821336014369196e+123	4.0379898751727945e+122
10	-4.7057251906386096e-297	3.181770513359429e-307	-2.1998622489132126e-305
9	-1.9544929856771155e+136	-7.948036635160632e+130	-2.5123246473038562e+135

Iters

Range

Point

3.1120206868224175e+122

4.821336014369196e+123

4.0379898751727945e+122

-4.7057251906386096e-297

3.181770513359429e-307

-2.1998622489132126e-305

-1.9544929856771155e+136

-7.948036635160632e+130

-2.5123246473038562e+135

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	133	88
1	133	88

end0.0ms (0%)

sample2.7s (36.4%)

Algorithm

1×

intervals

Results

294.0ms	5173×	body	128	valid
293.0ms	1145×	body	2048	valid
151.0ms	735×	body	1024	valid
124.0ms	380×	body	4096	valid
60.0ms	384×	body	512	valid
38.0ms	675×	body	128	nan
22.0ms	366×	body	128	invalid
19.0ms	183×	body	256	valid

Compiler

Compiled 1883 to 1421 computations (24.5% saved)

Details

analyze711.0ms (9.7%)

sample42.0ms (0.6%)

simplify280.0ms (3.8%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite31.0ms (0.4%)

series176.0ms (2.4%)

simplify69.0ms (0.9%)

prune104.0ms (1.4%)

localize13.0ms (0.2%)

rewrite51.0ms (0.7%)

series474.0ms (6.5%)

simplify79.0ms (1.1%)

prune181.0ms (2.5%)

localize12.0ms (0.2%)

rewrite35.0ms (0.5%)

series295.0ms (4%)

simplify77.0ms (1.1%)

prune116.0ms (1.6%)

localize11.0ms (0.2%)

rewrite25.0ms (0.3%)

series167.0ms (2.3%)

simplify45.0ms (0.6%)

prune68.0ms (0.9%)

regimes1.5s (20%)

bsearch111.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.7s (36.4%)

Profiling