Details

analyze464.0ms (7.9%)

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	175×	body	128	valid
9.0ms	29×	body	2048	valid
5.0ms	25×	body	1024	valid
4.0ms	14×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	23×	body	128	nan
1.0ms	13×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify410.0ms (6.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (316.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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: 33.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1805`
14×	`*-un-lft-identity_binary64_1783`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`add-cube-cbrt_binary64_1818` `add-log-exp_binary64_1822`
6×	`difference-of-squares_binary64_1752` `associate-/l*_binary64_1728` `sqrt-prod_binary64_1799` `times-frac_binary64_1789`
5×	`pow1_binary64_1844`
4×	`flip3--_binary64_1787` `cancel-sign-sub-inv_binary64_1749` `flip--_binary64_1758`
3×	`distribute-lft-out--_binary64_1735`
2×	`associate-/l/_binary64_1730` `diff-log_binary64_1875` `sqrt-div_binary64_1800` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `sub-neg_binary64_1776`
1×	`div-sub_binary64_1788` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `pow1/2_binary64_1863` `associate-/r*_binary64_1727` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series257.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune120.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 5.6b

Counts

87 → 8

Compiler

Compiled 2145 to 1281 computations (40.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1805`
18×	`*-un-lft-identity_binary64_1783`
14×	`add-cube-cbrt_binary64_1818`
13×	`associate-r_binary64_1723`
10×	`times-frac_binary64_1789`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`add-log-exp_binary64_1822`
7×	`pow1_binary64_1844`
6×	`associate-l_binary64_1724`
5×	`flip3--_binary64_1787` `sqrt-prod_binary64_1799` `flip--_binary64_1758`
4×	`difference-of-squares_binary64_1752` `cancel-sign-sub-inv_binary64_1749`
2×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `distribute-lft-out--_binary64_1735` `associate-*l/_binary64_1726` `diff-log_binary64_1875` `sqrt-div_binary64_1800` `frac-times_binary64_1793` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776`
1×	`associate-r/_binary64_1725` `div-inv_binary64_1780` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `-commutative_binary64_1714` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796`

Counts

4 → 83

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series262.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5360	2202

prune107.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	96	7	103

Merged error: 5.6b

Counts

103 → 7

Compiler

Compiled 2294 to 1372 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.6b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
15.4b	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
14×	`*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
13×	`add-sqr-sqrt_binary64_1805` `associate-r_binary64_1723`
12×	`add-cube-cbrt_binary64_1818` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
9×	`times-frac_binary64_1789`
8×	`add-log-exp_binary64_1822`
6×	`pow-prod-down_binary64_1854`
3×	`sqrt-prod_binary64_1799` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
2×	`flip3--_binary64_1787` `sqrt-div_binary64_1800` `flip--_binary64_1758`
1×	`associate-r/_binary64_1725` `+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `pow1/2_binary64_1863` `associate-l_binary64_1724` `diff-log_binary64_1875` `-commutative_binary64_1714` `sum-log_binary64_1874` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

4 → 77

Calls

4 calls:

10.0ms	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))
7.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series170.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
60.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
10.0ms	(.f64 (.f64 a (*.f64 c -4)) (/.f64 1/2 a))

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4936	1466
1	4936	1466

prune107.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	88	8	96

Merged error: 5.5b

Counts

96 → 8

Compiler

Compiled 2446 to 1474 computations (39.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.6b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1783`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`add-sqr-sqrt_binary64_1805` `add-log-exp_binary64_1822`
7×	`add-cube-cbrt_binary64_1818`
5×	`pow1_binary64_1844`
4×	`associate-/r*_binary64_1727` `times-frac_binary64_1789`
3×	`distribute-lft-out_binary64_1734` `sqrt-prod_binary64_1799`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `sqrt-div_binary64_1800` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`+-commutative_binary64_1713` `associate-/l*_binary64_1728` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `pow1/2_binary64_1863` `diff-log_binary64_1875` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

4 → 64

Calls

4 calls:

10.0ms	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
7.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series345.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(/.f64 (.f64 c -2) (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
63.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
36.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4951	1690
1	4951	1690

prune78.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	76	8	84

Merged error: 5.5b

Counts

84 → 8

Compiler

Compiled 1710 to 1005 computations (41.2% saved)

regimes810.0ms (13.7%)

Compiler: Compiled 4224 to 3216 computations (23.9% saved)

bsearch97.0ms (1.6%)

Steps

Iters	Range	Point
7	7.482650775739311e+127	6.940404749714049e+129	1.928533493233392e+129
9	4.1267928365631376e-194	6.602297926380012e-187	4.190818973144896e-194
7	-3.1670677211042097e+132	-3.885194447819339e+130	-3.475153330017618e+131

Iters

Range

Point

7.482650775739311e+127

6.940404749714049e+129

1.928533493233392e+129

4.1267928365631376e-194

6.602297926380012e-187

4.190818973144896e-194

-3.1670677211042097e+132

-3.885194447819339e+130

-3.475153330017618e+131

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	82
1	102	82

end0.0ms (0%)

sample2.2s (36.5%)

Algorithm

1×

intervals

Results

302.0ms	1171×	body	2048	valid
282.0ms	5164×	body	128	valid
142.0ms	702×	body	1024	valid
120.0ms	394×	body	4096	valid
57.0ms	385×	body	512	valid
35.0ms	703×	body	128	nan
22.0ms	380×	body	128	invalid
18.0ms	184×	body	256	valid

Compiler

Compiled 1148 to 862 computations (24.9% saved)

Details

analyze464.0ms (7.9%)

sample42.0ms (0.7%)

simplify410.0ms (6.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series257.0ms (4.4%)

simplify82.0ms (1.4%)

prune120.0ms (2%)

localize11.0ms (0.2%)

rewrite39.0ms (0.7%)

series262.0ms (4.4%)

simplify74.0ms (1.3%)

prune107.0ms (1.8%)

localize14.0ms (0.2%)

rewrite32.0ms (0.5%)

series170.0ms (2.9%)

simplify60.0ms (1%)

prune107.0ms (1.8%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series345.0ms (5.8%)

simplify72.0ms (1.2%)

prune78.0ms (1.3%)

regimes810.0ms (13.7%)

bsearch97.0ms (1.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (36.5%)

Profiling