Details

analyze1.6s (10.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4877	216
1	4877	216
0	3	3
1	3	3

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)

sample71.0ms (0.5%)

Algorithm

1×

intervals

Results

43.0ms	256×	body	128	valid
3.0ms	21×	body	128	nan
2.0ms	15×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify640.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (628.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune14.0ms (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

Error

21.5b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize43.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite57.0ms (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:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
11.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series1.0s (6.7%)

Counts

4 → 61

Calls

4 calls:

267.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
267.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
253.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
221.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 3806 to 2831 computations (25.6% saved)

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4928	2188
1	4928	2188

prune404.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	7	121

Error

6.0b

Counts

121 → 7

Compiler

Compiled 4995 to 2965 computations (40.6% saved)

localize42.0ms (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))))))
0.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite47.0ms (0.3%)

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:

15.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
8.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series1.1s (7.4%)

Counts

4 → 62

Calls

4 calls:

313.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
303.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
253.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
251.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))

Compiler

Compiled 2983 to 2297 computations (23% saved)

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4948	2660
1	4948	2660

prune355.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	135	6	141

Error

6.0b

Counts

141 → 6

Compiler

Compiled 4528 to 2498 computations (44.8% saved)

localize46.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
0.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite60.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`distribute-lft-out_binary64` `prod-exp_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

25.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series1.1s (7.4%)

Counts

4 → 62

Calls

4 calls:

314.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
299.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
261.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
243.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))

Compiler

Compiled 3135 to 2449 computations (21.9% saved)

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5052	2599

prune377.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	141	7	148

Error

6.0b

Counts

148 → 7

Compiler

Compiled 5011 to 2902 computations (42.1% saved)

localize50.0ms (0.3%)

Local error

Found 4 expressions with local error:

7.0b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

18.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
8.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
8.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series1.7s (11.4%)

Counts

4 → 60

Calls

4 calls:

587.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
423.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
422.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
282.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 5943 to 4434 computations (25.4% saved)

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5074	2821

prune440.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	115	7	122

Error

6.0b

Counts

122 → 7

Compiler

Compiled 6199 to 3721 computations (40% saved)

regimes1.2s (8.1%)

Accuracy

Total 0.8b remaining (13%)

Threshold costs 0.8b (13%)

Compiler

Compiled 6002 to 4310 computations (28.2% saved)

bsearch9.0ms (0.1%)

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

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	141	358
1	141	358

end0.0ms (0%)

sample4.1s (27.4%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
93.0ms	618×	body	128	nan
69.0ms	434×	body	128	invalid

Compiler

Compiled 1755 to 1235 computations (29.6% saved)

Details

analyze1.6s (10.7%)

sample71.0ms (0.5%)

simplify640.0ms (4.2%)

prune14.0ms (0.1%)

localize43.0ms (0.3%)

rewrite57.0ms (0.4%)

series1.0s (6.7%)

simplify113.0ms (0.7%)

prune404.0ms (2.7%)

localize42.0ms (0.3%)

rewrite47.0ms (0.3%)

series1.1s (7.4%)

simplify119.0ms (0.8%)

prune355.0ms (2.4%)

localize46.0ms (0.3%)

rewrite60.0ms (0.4%)

series1.1s (7.4%)

simplify119.0ms (0.8%)

prune377.0ms (2.5%)

localize50.0ms (0.3%)

rewrite44.0ms (0.3%)

series1.7s (11.4%)

simplify90.0ms (0.6%)

prune440.0ms (2.9%)

regimes1.2s (8.1%)

bsearch9.0ms (0.1%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample4.1s (27.4%)

Profiling