Details

analyze448.0ms (8.1%)

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)

sample35.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	183×	body	128	valid
8.0ms	33×	body	2048	valid
4.0ms	19×	body	1024	valid
2.0ms	8×	body	4096	valid
1.0ms	7×	body	512	valid
1.0ms	14×	body	128	invalid
1.0ms	13×	body	128	nan
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify434.0ms (7.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (336.0ms)

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

Error

31.2b

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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1783`
15×	`add-sqr-sqrt_binary64_1805`
14×	`add-cube-cbrt_binary64_1818`
12×	`times-frac_binary64_1789`
8×	`add-log-exp_binary64_1822`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
5×	`distribute-lft-out_binary64_1734` `pow1_binary64_1844`
4×	`associate-/l*_binary64_1728`
3×	`associate-/r*_binary64_1727` `sqrt-prod_binary64_1799`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `flip-+_binary64_1757` `sqrt-div_binary64_1800` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`+-commutative_binary64_1713` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `pow1/2_binary64_1863` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

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)))

series231.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
66.0ms	(+.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))))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune121.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Error

5.9b

Counts

85 → 8

Compiler

Compiled 2141 to 1155 computations (46.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
7.8b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
23.0b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.0b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_1822`
6×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `cbrt-prod_binary64_1814` `*-un-lft-identity_binary64_1783`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `cbrt-div_binary64_1815` `pow1_binary64_1844`
3×	`flip3--_binary64_1787` `flip--_binary64_1758`
2×	`pow1/3_binary64_1865`
1×	`+-commutative_binary64_1713` `flip-+_binary64_1757` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `sum-log_binary64_1874` `flip3-+_binary64_1786` `sub-neg_binary64_1776`

Counts

4 → 49

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))

series327.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
92.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
85.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4977	1572
1	4977	1572

prune93.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	61	8	69

Error

5.9b

Counts

69 → 8

Compiler

Compiled 2325 to 1303 computations (44% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1783`
8×	`add-sqr-sqrt_binary64_1805` `add-log-exp_binary64_1822`
6×	`add-cube-cbrt_binary64_1818` `sqrt-prod_binary64_1799` `pow1_binary64_1844`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `sqrt-div_binary64_1800`
2×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `pow1/2_binary64_1863` `sum-log_binary64_1874` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `flip--_binary64_1758`

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 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series233.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(+.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))))
56.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5082	1354

prune101.0ms (1.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Error

5.9b

Counts

74 → 8

Compiler

Compiled 2536 to 1377 computations (45.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1783`
8×	`add-sqr-sqrt_binary64_1805` `add-log-exp_binary64_1822`
6×	`add-cube-cbrt_binary64_1818` `sqrt-prod_binary64_1799` `pow1_binary64_1844`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `sqrt-div_binary64_1800`
2×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `pow1/2_binary64_1863` `sum-log_binary64_1874` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `flip--_binary64_1758`

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 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series249.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
60.0ms	(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)))))

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5082	1354

prune97.0ms (1.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	66	8	74

Error

5.9b

Counts

74 → 8

Compiler

Compiled 2450 to 1310 computations (46.5% saved)

regimes527.0ms (9.6%)

Accuracy

Total 3.4b remaining (37%)

Threshold costs 0b (0%)

Compiler

Compiled 3004 to 2222 computations (26% saved)

bsearch106.0ms (1.9%)

Steps

Iters	Range	Point
8	1.4321713852773844e+135	2.1090845602311984e+139	1.6833943237704546e+136
9	-1.8898449676445546e-99	-2.875154670333836e-106	-2.058574872602062e-105
8	-1.7915129492577403e+88	-1.3262247074219856e+85	-2.6479930097769547e+85

Iters

Range

Point

1.4321713852773844e+135

2.1090845602311984e+139

1.6833943237704546e+136

-1.8898449676445546e-99

-2.875154670333836e-106

-2.058574872602062e-105

-1.7915129492577403e+88

-1.3262247074219856e+85

-2.6479930097769547e+85

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	127	103
1	127	103

end0.0ms (0%)

sample2.1s (37.5%)

Algorithm

1×

intervals

Results

286.0ms	1143×	body	2048	valid
265.0ms	5236×	body	128	valid
132.0ms	686×	body	1024	valid
118.0ms	385×	body	4096	valid
52.0ms	374×	body	512	valid
30.0ms	619×	body	128	nan
22.0ms	392×	body	128	invalid
17.0ms	176×	body	256	valid

Compiler

Compiled 870 to 634 computations (27.1% saved)

Details

analyze448.0ms (8.1%)

sample35.0ms (0.6%)

simplify434.0ms (7.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite29.0ms (0.5%)

series231.0ms (4.2%)

simplify93.0ms (1.7%)

prune121.0ms (2.2%)

localize14.0ms (0.2%)

rewrite22.0ms (0.4%)

series327.0ms (5.9%)

simplify54.0ms (1%)

prune93.0ms (1.7%)

localize13.0ms (0.2%)

rewrite27.0ms (0.5%)

series233.0ms (4.2%)

simplify63.0ms (1.1%)

prune101.0ms (1.8%)

localize13.0ms (0.2%)

rewrite26.0ms (0.5%)

series249.0ms (4.5%)

simplify67.0ms (1.2%)

prune97.0ms (1.8%)

regimes527.0ms (9.6%)

bsearch106.0ms (1.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (37.5%)

Profiling