Details

analyze711.0ms (11.5%)

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)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
1.0ms	18×	body	128	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify448.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (350.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune7.0ms (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: 20.6b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `cancel-sign-sub-inv_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 → 59

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series252.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
63.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify119.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4907	1457
1	4907	1457

prune153.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	9	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 6.8b

Counts

72 → 9

Compiler

Compiled 3415 to 2057 computations (39.8% saved)

localize26.0ms (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)))))
3.9b	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
4.1b	(/.f64 (*.f64 c a) b)
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `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×	`associate-/l/_binary64` `flip3--_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

12.0ms	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
4.0ms	(/.f64 (*.f64 c a) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series182.0ms (3%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
52.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
51.0ms	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
17.0ms	(/.f64 (*.f64 c a) b)

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5074	1297

prune134.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Merged error: 5.9b

Counts

92 → 11

Compiler

Compiled 3526 to 1891 computations (46.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.4b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series316.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
56.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4897	1972
1	4897	1972

prune134.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 5.9b

Counts

95 → 10

Compiler

Compiled 3265 to 1649 computations (49.5% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))) c))
0.4b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
80×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-/r/_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 127

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series257.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))) c))
54.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
52.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
30.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify137.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4921	4182
1	4921	4182

prune206.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	139	10	149

Merged error: 5.9b

Counts

149 → 10

Compiler

Compiled 5346 to 2711 computations (49.3% saved)

regimes554.0ms (9%)

Compiler: Compiled 6282 to 4330 computations (31.1% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	126	412
1	126	412

end0.0ms (0%)

sample2.2s (35.2%)

Algorithm

1×

intervals

Results

686.0ms	8000×	body	128	valid
55.0ms	644×	body	128	nan
31.0ms	376×	body	128	invalid

Compiler

Compiled 1863 to 1256 computations (32.6% saved)

Details

analyze711.0ms (11.5%)

sample40.0ms (0.7%)

simplify448.0ms (7.3%)

prune7.0ms (0.1%)

localize29.0ms (0.5%)

rewrite27.0ms (0.4%)

series252.0ms (4.1%)

simplify119.0ms (1.9%)

prune153.0ms (2.5%)

localize26.0ms (0.4%)

rewrite29.0ms (0.5%)

series182.0ms (3%)

simplify41.0ms (0.7%)

prune134.0ms (2.2%)

localize19.0ms (0.3%)

rewrite26.0ms (0.4%)

series316.0ms (5.1%)

simplify78.0ms (1.3%)

prune134.0ms (2.2%)

localize21.0ms (0.3%)

rewrite35.0ms (0.6%)

series257.0ms (4.2%)

simplify137.0ms (2.2%)

prune206.0ms (3.4%)

regimes554.0ms (9%)

bsearch5.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.2s (35.2%)

Profiling