Details

analyze713.0ms (12%)

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	19×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify247.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune8.0ms (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: 19.9b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

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

series503.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
119.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4911	1445
1	4911	1445

prune145.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	6	69

Merged error: 6.5b

Counts

69 → 6

Compiler

Compiled 3126 to 1879 computations (39.9% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

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

series467.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4929	1379
1	4929	1379

prune164.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	69	6	75

Merged error: 6.5b

Counts

75 → 6

Compiler

Compiled 4143 to 2491 computations (39.9% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
3.3b	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `log-prod_binary64` `exp-sum_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64` `exp-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `log-pow_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 62

Calls

4 calls:

10.0ms	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)))
10.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series671.0ms (11.3%)

Counts

4 → 12

Calls

4 calls:

329.0ms	(exp.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)))
125.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
106.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify101.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4967	1561
1	4967	1561

prune145.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	73	7	80

Merged error: 5.9b

Counts

80 → 7

Compiler

Compiled 3521 to 2167 computations (38.5% saved)

localize32.0ms (0.5%)

Local error

Found 4 expressions with local error:

25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (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:

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

series487.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4925	1404
1	4925	1404

prune238.0ms (4%)

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: 5.9b

Counts

79 → 7

Compiler

Compiled 5436 to 3335 computations (38.6% saved)

regimes155.0ms (2.6%)

Compiler: Compiled 909 to 648 computations (28.7% saved)

bsearch94.0ms (1.6%)

Steps

Iters	Range		Point
9	3.631151000214039e+124	6.12439716154937e+130	1.3534209732535931e+128
10	-3.21829682074332e+120	-1.3939830885719518e+103	-9.753618941686308e+113

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	120	179
1	120	179

end0.0ms (0%)

sample1.3s (22.3%)

Algorithm

1×

intervals

Results

696.0ms	8000×	body	128	valid
60.0ms	689×	body	128	nan
37.0ms	419×	body	128	invalid

Compiler

Compiled 459 to 317 computations (30.9% saved)

Details

analyze713.0ms (12%)

sample41.0ms (0.7%)

simplify247.0ms (4.2%)

prune8.0ms (0.1%)

localize31.0ms (0.5%)

rewrite30.0ms (0.5%)

series503.0ms (8.5%)

simplify66.0ms (1.1%)

prune145.0ms (2.4%)

localize27.0ms (0.4%)

rewrite23.0ms (0.4%)

series467.0ms (7.9%)

simplify76.0ms (1.3%)

prune164.0ms (2.8%)

localize24.0ms (0.4%)

rewrite32.0ms (0.5%)

series671.0ms (11.3%)

simplify101.0ms (1.7%)

prune145.0ms (2.4%)

localize32.0ms (0.5%)

rewrite21.0ms (0.4%)

series487.0ms (8.2%)

simplify66.0ms (1.1%)

prune238.0ms (4%)

regimes155.0ms (2.6%)

bsearch94.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (22.3%)

Profiling