Details

analyze937.0ms (8.7%)

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)

sample42.0ms (0.4%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
2.0ms	25×	body	128	nan
1.0ms	14×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify336.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (329.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune9.0ms (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

22.2b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
25.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite233.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

22.2b

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` `flip--_binary64` `cancel-sign-sub-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `diff-log_binary64` `sub-neg_binary64` `distribute-lft-out--_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))))

Compiler

Compiled 2594 to 1526 computations (41.2% saved)

series962.0ms (8.9%)

Error

6.9b

Counts

4 → 66

Calls

4 calls:

261.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
251.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
203.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
178.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 5342 to 3824 computations (28.4% saved)

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5185	2200

prune229.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Error

6.8b

Counts

126 → 7

Compiler

Compiled 3596 to 2106 computations (41.4% saved)

localize23.0ms (0.2%)

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))))))
1.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
25.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite216.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

6.8b

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×	`sqrt-prod_binary64` `associate-/l*_binary64`
2×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_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))))

Compiler

Compiled 2683 to 1482 computations (44.8% saved)

series959.0ms (8.9%)

Error

6.8b

Counts

4 → 62

Calls

4 calls:

302.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
245.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
197.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
166.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 3668 to 2710 computations (26.1% saved)

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4940	2540
1	4940	2540

prune231.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	129	12	141

Error

6.8b

Counts

141 → 12

Compiler

Compiled 3347 to 1846 computations (44.8% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite312.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

6.8b

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×	`sqrt-prod_binary64` `unswap-sqr_binary64` `associate-l_binary64`
2×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64` `flip3-+_binary64` `flip-+_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `un-div-inv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3144 to 1702 computations (45.9% saved)

series970.0ms (9%)

Error

6.8b

Counts

4 → 62

Calls

4 calls:

304.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
247.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
195.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
159.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3875 to 2907 computations (25% saved)

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4949	2479
1	4949	2479

prune293.0ms (2.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	142	12	154

Error

6.8b

Counts

154 → 12

Compiler

Compiled 3460 to 1961 computations (43.3% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
25.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite261.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

6.8b

Rules

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

Counts

4 → 54

Calls

4 calls:

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

Compiler

Compiled 2766 to 1503 computations (45.7% saved)

series863.0ms (8%)

Error

6.8b

Counts

4 → 60

Calls

4 calls:

207.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
196.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
182.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
178.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 5680 to 3963 computations (30.2% saved)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5108	1830

prune306.0ms (2.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	113	13	126

Error

6.8b

Counts

126 → 13

Compiler

Compiled 3542 to 1917 computations (45.9% saved)

regimes1.6s (14.5%)

Accuracy

Total 1.5b remaining (20.5%)

Threshold costs 0b (0%)

Compiler

Compiled 16231 to 11624 computations (28.4% saved)

bsearch10.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	158	477
1	158	477

end12.0ms (0.1%)

Compiler: Compiled 315 to 194 computations (38.4% saved)

sample1.7s (15.6%)

Algorithm

1×

intervals

Results

695.0ms	8000×	body	128	valid
60.0ms	695×	body	128	nan
34.0ms	383×	body	128	invalid

Compiler

Compiled 896 to 606 computations (32.4% saved)

Details

analyze937.0ms (8.7%)

sample42.0ms (0.4%)

simplify336.0ms (3.1%)

prune9.0ms (0.1%)

localize29.0ms (0.3%)

rewrite233.0ms (2.2%)

series962.0ms (8.9%)

simplify61.0ms (0.6%)

prune229.0ms (2.1%)

localize23.0ms (0.2%)

rewrite216.0ms (2%)

series959.0ms (8.9%)

simplify70.0ms (0.6%)

prune231.0ms (2.1%)

localize25.0ms (0.2%)

rewrite312.0ms (2.9%)

series970.0ms (9%)

simplify76.0ms (0.7%)

prune293.0ms (2.7%)

localize34.0ms (0.3%)

rewrite261.0ms (2.4%)

series863.0ms (8%)

simplify53.0ms (0.5%)

prune306.0ms (2.8%)

regimes1.6s (14.5%)

bsearch10.0ms (0.1%)

simplify7.0ms (0.1%)

end12.0ms (0.1%)

sample1.7s (15.6%)

Profiling