Details

analyze479.0ms (7.3%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
8.0ms	24×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	10×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	28×	body	128	nan
1.0ms	11×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify433.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (344.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune5.0ms (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

30.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2124`
15×	`add-sqr-sqrt_binary64_2146`
14×	`add-cube-cbrt_binary64_2159`
12×	`times-frac_binary64_2130`
8×	`add-log-exp_binary64_2163`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`distribute-lft-out_binary64_2075` `pow1_binary64_2185`
4×	`associate-/l*_binary64_2069`
3×	`sqrt-prod_binary64_2140` `associate-/r*_binary64_2068`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-div_binary64_2141` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 72

Calls

4 calls:

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

series233.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
40.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune117.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Error

5.2b

Counts

85 → 7

Compiler

Compiled 2102 to 1132 computations (46.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.8b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
9.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_2130`
59×	`add-sqr-sqrt_binary64_2146`
44×	`*-un-lft-identity_binary64_2124`
30×	`add-cube-cbrt_binary64_2159`
27×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
14×	`difference-of-squares_binary64_2093`
13×	`associate-/l*_binary64_2069` `sqrt-prod_binary64_2140`
10×	`cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `div-exp_binary64_2175`
9×	`associate-/r*_binary64_2068`
7×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076`
6×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157`
5×	`pow1_binary64_2185`
2×	`clear-num_binary64_2123` `sqrt-div_binary64_2141` `frac-2neg_binary64_2135`
1×	`sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `associate-/l/_binary64_2071`

Counts

4 → 136

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series517.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
171.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
60.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify112.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5011	5032

prune213.0ms (3.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	147	8	155

Error

5.1b

Counts

155 → 8

Compiler

Compiled 4797 to 2552 computations (46.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.8b	(/.f64 (.f64 4 (/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))) a)
9.4b	(/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_2146`
23×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
17×	`*-un-lft-identity_binary64_2124`
11×	`add-cube-cbrt_binary64_2159`
9×	`sqrt-prod_binary64_2140` `associate-/r*_binary64_2068` `times-frac_binary64_2130`
8×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
6×	`difference-of-squares_binary64_2093` `cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163`
5×	`pow1_binary64_2185` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076`
2×	`clear-num_binary64_2123` `associate-/r/_binary64_2070` `associate-/l*_binary64_2069` `sqrt-div_binary64_2141` `div-inv_binary64_2121` `frac-2neg_binary64_2135`
1×	`sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `associate-*r/_binary64_2066` `associate-/l/_binary64_2071`

Counts

4 → 90

Calls

4 calls:

14.0ms	(/.f64 (.f64 4 (/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))) a)
11.0ms	(/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
10.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series489.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
165.0ms	(/.f64 (.f64 4 (/.f64 (.f64 a c) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))) a)
59.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4950	2566
1	4950	2566

prune121.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	102	8	110

Error

5.1b

Counts

110 → 8

Compiler

Compiled 2886 to 1582 computations (45.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_2130`
82×	`*-un-lft-identity_binary64_2124`
57×	`add-sqr-sqrt_binary64_2146`
56×	`add-cube-cbrt_binary64_2159`
18×	`associate-/r*_binary64_2068`
15×	`add-exp-log_binary64_2162`
13×	`distribute-lft-out_binary64_2075`
9×	`associate-/r/_binary64_2070` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
7×	`div-exp_binary64_2175`
6×	`pow1_binary64_2185`
5×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
3×	`cbrt-undiv_binary64_2158` `associate-/l*_binary64_2069` `sqrt-prod_binary64_2140`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-div_binary64_2141` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`clear-num_binary64_2123` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `inv-pow_binary64_2209` `frac-2neg_binary64_2135`

Counts

4 → 135

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 a (+.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)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series257.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4904	4499
1	4904	4499

prune174.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	147	8	155

Error

5.1b

Counts

155 → 8

Compiler

Compiled 4125 to 2264 computations (45.1% saved)

regimes633.0ms (9.6%)

Accuracy

Total 1.2b remaining (16.7%)

Threshold costs 0b (0%)

Compiler

Compiled 4402 to 3234 computations (26.5% saved)

bsearch115.0ms (1.7%)

Steps

Iters	Range	Point
9	1.3757201747748946e+122	4.2744175307429915e+127	4.506449921036379e+122
8	-5.094737738097033e-276	-1.1972161547110289e-278	-1.2572184622052755e-278
9	-8.994821103457546e+83	-5.5446932295606685e+78	-6.936942472764157e+83

Iters

Range

Point

1.3757201747748946e+122

4.2744175307429915e+127

4.506449921036379e+122

-5.094737738097033e-276

-1.1972161547110289e-278

-1.2572184622052755e-278

-8.994821103457546e+83

-5.5446932295606685e+78

-6.936942472764157e+83

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	121	91
1	121	91

end0.0ms (0%)

sample2.2s (32.9%)

Algorithm

1×

intervals

Results

295.0ms	5280×	body	128	valid
289.0ms	1081×	body	2048	valid
148.0ms	716×	body	1024	valid
129.0ms	395×	body	4096	valid
52.0ms	341×	body	512	valid
34.0ms	656×	body	128	nan
22.0ms	419×	body	128	invalid
19.0ms	187×	body	256	valid

Compiler

Compiled 1198 to 873 computations (27.1% saved)

Details

analyze479.0ms (7.3%)

sample41.0ms (0.6%)

simplify433.0ms (6.6%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite30.0ms (0.5%)

series233.0ms (3.5%)

simplify98.0ms (1.5%)

prune117.0ms (1.8%)

localize13.0ms (0.2%)

rewrite54.0ms (0.8%)

series517.0ms (7.9%)

simplify112.0ms (1.7%)

prune213.0ms (3.2%)

localize14.0ms (0.2%)

rewrite48.0ms (0.7%)

series489.0ms (7.4%)

simplify70.0ms (1.1%)

prune121.0ms (1.8%)

localize13.0ms (0.2%)

rewrite42.0ms (0.6%)

series257.0ms (3.9%)

simplify85.0ms (1.3%)

prune174.0ms (2.6%)

regimes633.0ms (9.6%)

bsearch115.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (32.9%)

Profiling