Details

analyze531.0ms (5.6%)

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)

sample48.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
2.0ms	17×	body	128	invalid
2.0ms	21×	body	128	nan

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify451.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (349.0ms)

Iter	Nodes	Cost
0	2977	54
1	2977	54

prune17.0ms (0.2%)

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

21.9b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
0.0b	(.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite28.0ms (0.3%)

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

8 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))))
0.0ms	(.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))

series510.0ms (5.4%)

Counts

4 → 63

Calls

4 calls:

140.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
137.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
107.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 3661 to 2721 computations (25.7% saved)

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5026	2255

prune309.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Error

4.4b

Counts

123 → 7

Compiler

Compiled 5130 to 2981 computations (41.9% saved)

localize21.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
0.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.0b	(.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
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)))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite26.0ms (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

8 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))))
0.0ms	(.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))

series623.0ms (6.6%)

Counts

4 → 73

Calls

4 calls:

201.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
155.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
139.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
129.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 3253 to 2516 computations (22.7% saved)

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5086	3020

prune223.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	145	7	152

Error

4.4b

Counts

152 → 7

Compiler

Compiled 5027 to 2708 computations (46.1% saved)

localize22.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
0.2b	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
0.1b	(/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.0b	(.f64 -2 (.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))))
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)))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite34.0ms (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

8 calls:

14.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
6.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
6.0ms	(+.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))))
0.0ms	(.f64 -2 (.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))))

series612.0ms (6.4%)

Counts

4 → 73

Calls

4 calls:

194.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))
161.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 3409 to 2672 computations (21.6% saved)

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4941	2959
1	4941	2959

prune235.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	153	7	160

Error

4.4b

Counts

160 → 7

Compiler

Compiled 5505 to 3111 computations (43.5% saved)

localize26.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
0.0b	(sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.0b	(sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
0.0b	(.f64 -2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 54

Calls

8 calls:

7.0ms	(+.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
0.0ms	(.f64 -2 (.f64 (/.f64 1 (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (/.f64 c (sqrt.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))))))))

series607.0ms (6.4%)

Counts

4 → 80

Calls

4 calls:

160.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
159.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
144.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
144.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 5244 to 3936 computations (24.9% saved)

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4917	2668
1	4917	2668

prune285.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	134	7	141

Error

4.4b

Counts

141 → 7

Compiler

Compiled 6574 to 3671 computations (44.2% saved)

simplify31.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	458	2230
1	458	2230

regimes551.0ms (5.8%)

Compiler: Compiled 4437 to 3204 computations (27.8% saved)

bsearch84.0ms (0.9%)

Steps

Iters	Range		Point
9	9.615903331653504e+62	2.187501754633164e+68	1.4016155324368643e+68
10	-4.176701788223575e+165	-1.755158361384398e+153	-4.260328883394221e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes214.0ms (2.2%)

Compiler: Compiled 1008 to 822 computations (18.5% saved)

bsearch152.0ms (1.6%)

Steps

Iters	Range		Point
9	9.615903331653504e+62	2.187501754633164e+68	1.034882824210658e+67
11	-7.698649498808173e-291	1.2911959617105335e-301	3.48443996820576e-310
10	-4.176701788223575e+165	-1.755158361384398e+153	-4.663800766323179e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes164.0ms (1.7%)

Compiler: Compiled 819 to 684 computations (16.5% saved)

bsearch71.0ms (0.7%)

Steps

Iters	Range		Point
6	1.7442167395081463e-67	1.9828782542260833e-66	7.90893378423439e-67
10	-4.176701788223575e+165	-1.755158361384398e+153	-1.2307022757970055e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes166.0ms (1.7%)

Compiler: Compiled 723 to 612 computations (15.4% saved)

bsearch134.0ms (1.4%)

Steps

Iters	Range		Point
6	1.7442167395081463e-67	1.9828782542260833e-66	8.2330230629281e-67
11	-7.698649498808173e-291	1.2911959617105335e-301	3.48443996820576e-310
10	-4.176701788223575e+165	-1.755158361384398e+153	-2.2594982150455963e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes102.0ms (1.1%)

Compiler: Compiled 642 to 552 computations (14% saved)

bsearch28.0ms (0.3%)

Steps

Iters	Range		Point
6	1.7442167395081463e-67	1.9828782542260833e-66	7.260755226846968e-67

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes96.0ms (1%)

Compiler: Compiled 564 to 489 computations (13.3% saved)

bsearch31.0ms (0.3%)

Steps

Iters	Range		Point
6	1.7442167395081463e-67	1.9828782542260833e-66	1.756015759140486e-66

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes83.0ms (0.9%)

Compiler: Compiled 420 to 372 computations (11.4% saved)

bsearch32.0ms (0.3%)

Steps

Iters	Range		Point
6	1.7442167395081463e-67	1.9828782542260833e-66	1.946772538691715e-67

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes50.0ms (0.5%)

Compiler: Compiled 354 to 318 computations (10.2% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.3%)

Accuracy

Total 1.2b remaining (19%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch19.0ms (0.2%)

Compiler: Compiled 537 to 352 computations (34.5% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	168	745
1	168	745

end0.0ms (0%)

sample2.5s (26%)

Algorithm

1×

intervals

Results

714.0ms	8000×	body	128	valid
52.0ms	623×	body	128	nan
35.0ms	395×	body	128	invalid

Compiler

Compiled 2017 to 1430 computations (29.1% saved)

Pareto

0.4653043098640543

Details

analyze531.0ms (5.6%)

sample48.0ms (0.5%)

simplify451.0ms (4.7%)

prune17.0ms (0.2%)

localize24.0ms (0.2%)

rewrite28.0ms (0.3%)

series510.0ms (5.4%)

simplify62.0ms (0.7%)

prune309.0ms (3.2%)

localize21.0ms (0.2%)

rewrite26.0ms (0.3%)

series623.0ms (6.6%)

simplify68.0ms (0.7%)

prune223.0ms (2.3%)

localize22.0ms (0.2%)

rewrite34.0ms (0.4%)

series612.0ms (6.4%)

simplify88.0ms (0.9%)

prune235.0ms (2.5%)

localize26.0ms (0.3%)

rewrite24.0ms (0.3%)

series607.0ms (6.4%)

simplify117.0ms (1.2%)

prune285.0ms (3%)

simplify31.0ms (0.3%)

regimes551.0ms (5.8%)

bsearch84.0ms (0.9%)

regimes214.0ms (2.2%)

bsearch152.0ms (1.6%)

regimes164.0ms (1.7%)

bsearch71.0ms (0.7%)

regimes166.0ms (1.7%)

bsearch134.0ms (1.4%)

regimes102.0ms (1.1%)

bsearch28.0ms (0.3%)

regimes96.0ms (1%)

bsearch31.0ms (0.3%)

regimes83.0ms (0.9%)

bsearch32.0ms (0.3%)

regimes50.0ms (0.5%)

bsearch0.0ms (0%)

regimes25.0ms (0.3%)

bsearch19.0ms (0.2%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample2.5s (26%)

Profiling