Details

analyze731.0ms (12.2%)

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 (0.7%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
2.0ms	21×	body	128	nan
1.0ms	12×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify250.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

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: 22.6b

Counts

2 → 1

Compiler

Compiled 148 to 102 computations (31.1% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite35.0ms (0.6%)

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:

11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
9.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series525.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
142.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
124.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4860	1694
1	4860	1694

prune409.0ms (6.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Merged error: 8.6b

Counts

81 → 7

Compiler

Compiled 9657 to 6156 computations (36.3% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

7.6b	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
8×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64` `neg-log_binary64` `difference-of-squares_binary64`

Counts

4 → 60

Calls

4 calls:

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

series480.0ms (8%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
106.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5064	1506

prune181.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Merged error: 8.6b

Counts

79 → 7

Compiler

Compiled 4509 to 2664 computations (40.9% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`

Counts

4 → 60

Calls

4 calls:

7.0ms	(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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series480.0ms (8%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4932	1404
1	4932	1404

prune238.0ms (4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Merged error: 8.6b

Counts

79 → 7

Compiler

Compiled 5756 to 3413 computations (40.7% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.1b	(/.f64 (*.f64 a c) b)
5.3b	(/.f64 (+.f64 (neg.f64 b) (-.f64 (.f64 2 (/.f64 (.f64 a c) b)) b)) (*.f64 2 a))
26.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `times-frac_binary64`
7×	`sqrt-prod_binary64`
6×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`distribute-rgt-neg-in_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `associate-+r-_binary64` `pow1/2_binary64` `associate--l-_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `flip-+_binary64`

Counts

4 → 88

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (neg.f64 b) (-.f64 (.f64 2 (/.f64 (.f64 a c) b)) b)) (*.f64 2 a))
13.0ms	(-.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)))

series366.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
89.0ms	(/.f64 (+.f64 (neg.f64 b) (-.f64 (.f64 2 (/.f64 (.f64 a c) b)) b)) (*.f64 2 a))
32.0ms	(/.f64 (*.f64 a c) b)

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4926	1899
1	4926	1899

prune250.0ms (4.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	2	1	3
Picked	1	0	1
Done	1	2	3
Total	100	7	107

Merged error: 7.5b

Counts

107 → 7

Compiler

Compiled 6211 to 3575 computations (42.4% saved)

regimes137.0ms (2.3%)

Compiler: Compiled 930 to 642 computations (31% saved)

bsearch86.0ms (1.4%)

Steps

Iters	Range		Point
8	1.723717435094096e+56	2.017795699778576e+60	1.97543087619704e+60
9	-430611.2890384929	-1.1707958582698768	-425882.49394125835

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	158	178
1	158	178

end0.0ms (0%)

sample1.3s (21.5%)

Algorithm

1×

intervals

Results

695.0ms	8000×	body	128	valid
51.0ms	643×	body	128	nan
34.0ms	383×	body	128	invalid

Compiler

Compiled 465 to 311 computations (33.1% saved)

Details

analyze731.0ms (12.2%)

sample41.0ms (0.7%)

simplify250.0ms (4.2%)

prune17.0ms (0.3%)

localize24.0ms (0.4%)

rewrite35.0ms (0.6%)

series525.0ms (8.7%)

simplify99.0ms (1.6%)

prune409.0ms (6.8%)

localize24.0ms (0.4%)

rewrite24.0ms (0.4%)

series480.0ms (8%)

simplify70.0ms (1.2%)

prune181.0ms (3%)

localize27.0ms (0.4%)

rewrite23.0ms (0.4%)

series480.0ms (8%)

simplify68.0ms (1.1%)

prune238.0ms (4%)

localize26.0ms (0.4%)

rewrite41.0ms (0.7%)

series366.0ms (6.1%)

simplify65.0ms (1.1%)

prune250.0ms (4.1%)

regimes137.0ms (2.3%)

bsearch86.0ms (1.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.3s (21.5%)

Profiling