Details

analyze465.0ms (6.3%)

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
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 (0.5%)

Algorithm

1×

intervals

Results

10.0ms	175×	body	128	valid
8.0ms	30×	body	2048	valid
6.0ms	18×	body	4096	valid
3.0ms	17×	body	1024	valid
1.0ms	10×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	12×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify307.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (300.0ms)

Iter	Nodes	Cost
0	1706	24
1	1706	24

prune9.0ms (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: 31.7b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (.f64 3 a) c)
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
4×	`cancel-sign-sub-inv_binary64` `sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
7.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series344.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
28.0ms	(.f64 (.f64 3 a) c)

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4917	1226
1	4917	1226

prune428.0ms (5.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	61	13	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	13	75

Merged error: 10.1b

Counts

75 → 13

Compiler

Compiled 7812 to 5633 computations (27.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
2.1b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
8.0b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`distribute-lft-out_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 102

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
13.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.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)))

series874.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

390.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
290.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4939	3160
1	4939	3160

prune898.0ms (12.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	104	10	114
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	110	17	127

Merged error: 9.2b

Counts

127 → 17

Compiler

Compiled 17611 to 12801 computations (27.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (.f64 3 a) c)
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series356.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
30.0ms	(.f64 (.f64 3 a) c)

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4862	1126
1	4862	1126

prune210.0ms (2.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	70	16	86

Merged error: 7.4b

Counts

86 → 16

Compiler

Compiled 4027 to 2947 computations (26.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3))))) (*.f64 1 (/.f64 -1 c))))
0.7b	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))))
0.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
22.8b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`prod-exp_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`div-exp_binary64`
5×	`flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `flip-+_binary64`
4×	`associate-*r/_binary64` `rec-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/l*_binary64` `times-frac_binary64` `pow-flip_binary64` `sqrt-prod_binary64`
2×	`+-commutative_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 76

Calls

4 calls:

16.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3))))) (*.f64 1 (/.f64 -1 c))))
7.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

series617.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

297.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -3))))) (*.f64 1 (/.f64 -1 c))))
131.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))))
113.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))
76.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4954	1849
1	4954	1849

prune284.0ms (3.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 4.7b

Counts

104 → 12

Compiler

Compiled 5496 to 3963 computations (27.9% saved)

regimes449.0ms (6.1%)

Compiler: Compiled 1161 to 938 computations (19.2% saved)

bsearch102.0ms (1.4%)

Steps

Iters	Range	Point
9	9.868844952462997e+78	1.5786806145329016e+84	7.800968894528171e+82
9	-4.000051374170694e-144	-4.0341116064183935e-150	-4.081630763126819e-150
5	-4.584782125224332e+92	-1.9624486649854942e+92	-2.900085283291066e+92

Iters

Range

Point

9.868844952462997e+78

1.5786806145329016e+84

7.800968894528171e+82

-4.000051374170694e-144

-4.0341116064183935e-150

-4.081630763126819e-150

-4.584782125224332e+92

-1.9624486649854942e+92

-2.900085283291066e+92

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	170	124
1	170	124

end0.0ms (0%)

sample1.5s (20.2%)

Algorithm

1×

intervals

Results

292.0ms	5233×	body	128	valid
285.0ms	1102×	body	2048	valid
150.0ms	725×	body	1024	valid
125.0ms	363×	body	4096	valid
60.0ms	382×	body	512	valid
38.0ms	739×	body	128	nan
22.0ms	400×	body	128	invalid
20.0ms	195×	body	256	valid

Compiler

Compiled 358 to 273 computations (23.7% saved)

Details

analyze465.0ms (6.3%)

sample40.0ms (0.5%)

simplify307.0ms (4.1%)

prune9.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.5%)

series344.0ms (4.6%)

simplify62.0ms (0.8%)

prune428.0ms (5.8%)

localize13.0ms (0.2%)

rewrite56.0ms (0.8%)

series874.0ms (11.8%)

simplify77.0ms (1%)

prune898.0ms (12.1%)

localize17.0ms (0.2%)

rewrite29.0ms (0.4%)

series356.0ms (4.8%)

simplify62.0ms (0.8%)

prune210.0ms (2.8%)

localize17.0ms (0.2%)

rewrite42.0ms (0.6%)

series617.0ms (8.3%)

simplify115.0ms (1.5%)

prune284.0ms (3.8%)

regimes449.0ms (6.1%)

bsearch102.0ms (1.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.5s (20.2%)

Profiling