Details

analyze463.0ms (8.8%)

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)

sample40.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	177×	body	128	valid
6.0ms	25×	body	2048	valid
5.0ms	23×	body	1024	valid
4.0ms	14×	body	4096	valid
2.0ms	13×	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)

simplify359.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (271.0ms)

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: 30.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1805`
10×	`pow1_binary64_1844`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `*-un-lft-identity_binary64_1783`
8×	`add-log-exp_binary64_1822`
7×	`add-cube-cbrt_binary64_1818`
4×	`cancel-sign-sub-inv_binary64_1749` `sqrt-prod_binary64_1799`
3×	`flip3--_binary64_1787` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854` `flip--_binary64_1758` `associate-r_binary64_1723`
2×	`difference-of-squares_binary64_1752` `diff-log_binary64_1875` `sqrt-div_binary64_1800` `sub-neg_binary64_1776`
1×	`pow1/2_binary64_1863` `distribute-lft-out--_binary64_1735` `associate-l_binary64_1724` `*-commutative_binary64_1714` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`

Counts

4 → 62

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series181.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
64.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
15.0ms	(.f64 (.f64 3 a) c)

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune107.0ms (2%)

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: 10.3b

Counts

75 → 10

Compiler

Compiled 1784 to 1087 computations (39.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 a c))
0.4b	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)
19.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1805`
10×	`pow1_binary64_1844`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `*-un-lft-identity_binary64_1783`
8×	`add-log-exp_binary64_1822`
7×	`add-cube-cbrt_binary64_1818`
4×	`cancel-sign-sub-inv_binary64_1749` `sqrt-prod_binary64_1799`
3×	`flip3--_binary64_1787` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `associate-l_binary64_1724` `pow-prod-down_binary64_1854` `flip--_binary64_1758`
2×	`difference-of-squares_binary64_1752` `diff-log_binary64_1875` `sqrt-div_binary64_1800` `sub-neg_binary64_1776`
1×	`pow1/2_binary64_1863` `distribute-lft-out--_binary64_1735` `-commutative_binary64_1714` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `associate-r*_binary64_1723`

Counts

4 → 62

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)
5.0ms	(.f64 3 (.f64 a c))
4.0ms	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

series177.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))
63.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)
33.0ms	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
14.0ms	(.f64 3 (.f64 a c))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5420	1224

prune85.0ms (1.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	74	10	84

Merged error: 10.3b

Counts

84 → 10

Compiler

Compiled 1770 to 1000 computations (43.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
19.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1805`
12×	`*-un-lft-identity_binary64_1783`
8×	`add-cube-cbrt_binary64_1818` `sqrt-prod_binary64_1799` `add-log-exp_binary64_1822`
6×	`cancel-sign-sub-inv_binary64_1749` `pow1_binary64_1844`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `add-exp-log_binary64_1821` `sqrt-div_binary64_1800` `flip--_binary64_1758`
2×	`pow1/2_binary64_1863` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

4 → 64

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series230.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
58.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5062	1560

prune129.0ms (2.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	76	10	86

Merged error: 10.3b

Counts

86 → 10

Compiler

Compiled 3008 to 1803 computations (40.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.7b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
19.8b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
19.8b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_1822`
7×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`cbrt-prod_binary64_1814`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `cbrt-div_binary64_1815` `cancel-sign-sub-inv_binary64_1749` `flip--_binary64_1758` `pow1_binary64_1844`
2×	`diff-log_binary64_1875` `pow1/3_binary64_1865` `sub-neg_binary64_1776`

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series327.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
97.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
87.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4918	1581
1	4918	1581

prune97.0ms (1.8%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	5	6
Picked	0	1	1
Done	0	3	3
Total	63	11	74

Merged error: 10.3b

Counts

74 → 11

Compiler

Compiled 2297 to 1402 computations (39% saved)

regimes644.0ms (12.2%)

Compiler: Compiled 4445 to 3426 computations (22.9% saved)

bsearch105.0ms (2%)

Steps

Iters	Range	Point
8	3.0018031175744667e+139	3.5583495127587305e+142	3.816879541232831e+141
8	1.957200319709918e-117	1.7923797599146023e-113	1.9979259851056098e-117
9	-2.1284436423706146e+155	-2.8882740537708103e+149	-1.3337681397070838e+154

Iters

Range

Point

3.0018031175744667e+139

3.5583495127587305e+142

3.816879541232831e+141

1.957200319709918e-117

1.7923797599146023e-113

1.9979259851056098e-117

-2.1284436423706146e+155

-2.8882740537708103e+149

-1.3337681397070838e+154

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	100	113
1	100	113

end0.0ms (0%)

sample1.9s (36.1%)

Algorithm

1×

intervals

Results

279.0ms	5204×	body	128	valid
277.0ms	1104×	body	2048	valid
152.0ms	736×	body	1024	valid
125.0ms	393×	body	4096	valid
58.0ms	367×	body	512	valid
35.0ms	701×	body	128	nan
20.0ms	380×	body	128	invalid
20.0ms	196×	body	256	valid

Compiler

Compiled 880 to 668 computations (24.1% saved)

Details

analyze463.0ms (8.8%)

sample40.0ms (0.8%)

simplify359.0ms (6.8%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite29.0ms (0.5%)

series181.0ms (3.4%)

simplify67.0ms (1.3%)

prune107.0ms (2%)

localize12.0ms (0.2%)

rewrite28.0ms (0.5%)

series177.0ms (3.4%)

simplify62.0ms (1.2%)

prune85.0ms (1.6%)

localize16.0ms (0.3%)

rewrite33.0ms (0.6%)

series230.0ms (4.4%)

simplify69.0ms (1.3%)

prune129.0ms (2.4%)

localize14.0ms (0.3%)

rewrite29.0ms (0.5%)

series327.0ms (6.2%)

simplify50.0ms (1%)

prune97.0ms (1.8%)

regimes644.0ms (12.2%)

bsearch105.0ms (2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (36.1%)

Profiling