Details

analyze720.0ms (11.3%)

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
2.0ms	23×	body	128	nan
1.0ms	12×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify250.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune17.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 20.0b

Counts

2 → 1

Compiler

Compiled 148 to 102 computations (31.1% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`add-log-exp_binary64`
10×	`sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `associate--l-_binary64` `associate-+l-_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 68

Calls

4 calls:

16.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
11.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series509.0ms (8%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
138.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
122.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4860	1694
1	4860	1694

prune431.0ms (6.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	8	81

Merged error: 8.0b

Counts

81 → 8

Compiler

Compiled 10087 to 6495 computations (35.6% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

8.0b	(-.f64 (neg.f64 b) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`sqrt-prod_binary64`
2×	`diff-log_binary64` `pow1/3_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64`

Counts

4 → 55

Calls

4 calls:

6.0ms	(-.f64 (neg.f64 b) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series678.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(-.f64 (neg.f64 b) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
169.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
157.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4945	1854
1	4945	1854

prune179.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	67	8	75

Merged error: 8.0b

Counts

75 → 8

Compiler

Compiled 4536 to 2723 computations (40% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

5.4b	(-.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`cbrt-prod_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `neg-sub0_binary64` `pow1/3_binary64` `cancel-sign-sub-inv_binary64` `neg-log_binary64`

Counts

4 → 57

Calls

4 calls:

6.0ms	(-.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series560.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
146.0ms	(-.f64 (neg.f64 b) (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4854	1435
1	4854	1435

prune168.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	69	8	77

Merged error: 8.0b

Counts

77 → 8

Compiler

Compiled 4275 to 2520 computations (41.1% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0b	(/.f64 (.f64 2 c) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
6.0b	(/.f64 (*.f64 a c) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r*_binary64` `times-frac_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (.f64 2 c) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series370.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
103.0ms	(/.f64 (.f64 2 c) (.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)))
35.0ms	(/.f64 (*.f64 a c) b)

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4959	1325
1	4959	1325

prune347.0ms (5.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	86	8	94

Merged error: 7.0b

Counts

94 → 8

Compiler

Compiled 8365 to 5201 computations (37.8% saved)

regimes205.0ms (3.2%)

Compiler: Compiled 1422 to 998 computations (29.8% saved)

bsearch69.0ms (1.1%)

Steps

Iters	Range		Point
4	8.163347463333852e+96	1.4758277851489848e+97	1.4104321813817429e+97
9	-1.403527244514743e+138	-6.940841064143257e+130	-1.3504945223411428e+138

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	117	168
1	117	168

end0.0ms (0%)

sample1.3s (20.5%)

Algorithm

1×

intervals

Results

694.0ms	8000×	body	128	valid
58.0ms	665×	body	128	nan
31.0ms	376×	body	128	invalid

Compiler

Compiled 486 to 334 computations (31.3% saved)

Details

analyze720.0ms (11.3%)

sample41.0ms (0.6%)

simplify250.0ms (3.9%)

prune17.0ms (0.3%)

localize24.0ms (0.4%)

rewrite45.0ms (0.7%)

series509.0ms (8%)

simplify101.0ms (1.6%)

prune431.0ms (6.7%)

localize30.0ms (0.5%)

rewrite22.0ms (0.3%)

series678.0ms (10.6%)

simplify75.0ms (1.2%)

prune179.0ms (2.8%)

localize30.0ms (0.5%)

rewrite21.0ms (0.3%)

series560.0ms (8.8%)

simplify86.0ms (1.3%)

prune168.0ms (2.6%)

localize27.0ms (0.4%)

rewrite36.0ms (0.6%)

series370.0ms (5.8%)

simplify41.0ms (0.6%)

prune347.0ms (5.4%)

regimes205.0ms (3.2%)

bsearch69.0ms (1.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.3s (20.5%)

Profiling