Details

analyze991.0ms (17%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	52
1	67	52
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	200×	body	128	valid
7.0ms	25×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	12×	body	1024	valid
2.0ms	7×	body	4096	valid
1.0ms	8×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

12.3b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
15.4b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_1822` `pow1_binary64_1844`
7×	`*-un-lft-identity_binary64_1783`
6×	`add-sqr-sqrt_binary64_1805`
5×	`add-cube-cbrt_binary64_1818`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `flip-+_binary64_1757` `sqrt-prod_binary64_1799` `sqrt-div_binary64_1800` `flip3-+_binary64_1786`
3×	`sqrt-pow1_binary64_1801`
2×	`associate-*r/_binary64_1725` `+-commutative_binary64_1713` `pow1/2_binary64_1863` `sum-log_binary64_1874`
1×	`distribute-lft-out_binary64_1734` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796`

Counts

4 → 51

Calls

4 calls:

13.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
5.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

series186.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
39.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
25.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
22.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4937	1285
1	4937	1285

prune100.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	52	11	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	11	64

Error

12.1b

Counts

64 → 11

Compiler

Compiled 1644 to 1129 computations (31.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
0.6b	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
15.4b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
8×	`add-sqr-sqrt_binary64_1805`
7×	`add-cube-cbrt_binary64_1818`
6×	`add-log-exp_binary64_1822`
5×	`log-pow_binary64_1872` `sqrt-prod_binary64_1799`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `sqrt-div_binary64_1800` `exp-prod_binary64_1835`
3×	`log-prod_binary64_1869` `flip-+_binary64_1757` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801`
2×	`associate-*r/_binary64_1725` `pow1/2_binary64_1863`
1×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `sum-log_binary64_1874` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796` `rem-log-exp_binary64_1824`

Counts

4 → 56

Calls

4 calls:

14.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
2.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))

series280.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
92.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
40.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
24.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4893	1559
1	4893	1559

prune109.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	66	13	79

Error

12.1b

Counts

79 → 13

Compiler

Compiled 1986 to 1406 computations (29.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))) 3))
0.5b	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))) 3)
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
15.4b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-prod_binary64_1814`
13×	`*-un-lft-identity_binary64_1783`
12×	`add-sqr-sqrt_binary64_1805`
11×	`add-cube-cbrt_binary64_1818`
9×	`pow1_binary64_1844`
8×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
7×	`sqrt-prod_binary64_1799`
6×	`sqrt-div_binary64_1800` `add-log-exp_binary64_1822`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
4×	`associate-*r/_binary64_1725` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow-pow_binary64_1855` `cube-div_binary64_1812`
3×	`pow-unpow_binary64_1860` `sqrt-pow1_binary64_1801`
2×	`sqr-pow_binary64_1755` `cube-mult_binary64_1813` `unpow3_binary64_1849` `cbrt-div_binary64_1815` `pow1/2_binary64_1863`
1×	`+-commutative_binary64_1713` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `distribute-lft-out_binary64_1734` `sum-log_binary64_1874` `pow1/3_binary64_1865` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796` `pow-to-exp_binary64_1852` `sqrt-pow2_binary64_1802` `pow-exp_binary64_1851`

Counts

4 → 83

Calls

4 calls:

15.0ms	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))) 3)
12.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
3.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))) 3))

series355.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))) 3)
101.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))) 3))
39.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
23.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	2595
1	4962	2595

prune144.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	95	13	108

Error

12.1b

Counts

108 → 13

Compiler

Compiled 2817 to 1983 computations (29.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
0.3b	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
15.4b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1805`
18×	`sqrt-prod_binary64_1799`
16×	`*-un-lft-identity_binary64_1783`
10×	`add-cube-cbrt_binary64_1818` `pow1_binary64_1844`
7×	`associate-r_binary64_1723`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `sqrt-div_binary64_1800` `add-log-exp_binary64_1822`
4×	`flip-+_binary64_1757` `pow1/2_binary64_1863` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `unswap-sqr_binary64_1751`
3×	`distribute-lft-out_binary64_1734` `pow-prod-down_binary64_1854`
2×	`associate-*r/_binary64_1725` `rem-sqrt-square_binary64_1796`
1×	`+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `*-commutative_binary64_1714` `sum-log_binary64_1874`

Counts

4 → 76

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
12.0ms	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series250.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
84.0ms	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
42.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
25.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify101.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5113	2192

prune112.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	88	13	101

Error

12.1b

Counts

101 → 13

Compiler

Compiled 2176 to 1494 computations (31.3% saved)

regimes557.0ms (9.5%)

Accuracy

Total 0.2b remaining (1.9%)

Threshold costs 0.2b (1.9%)

Compiler

Compiled 6427 to 5256 computations (18.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	30
1	23	30

end0.0ms (0%)

sample2.1s (36.2%)

Algorithm

1×

intervals

Results

354.0ms	6114×	body	128	valid
231.0ms	784×	body	2048	valid
160.0ms	8000×	pre	128	true
123.0ms	524×	body	1024	valid
88.0ms	234×	body	4096	valid
40.0ms	225×	body	512	valid
13.0ms	119×	body	256	valid

Compiler

Compiled 912 to 740 computations (18.9% saved)

Details

analyze991.0ms (17%)

sample40.0ms (0.7%)

simplify8.0ms (0.1%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

rewrite41.0ms (0.7%)

series186.0ms (3.2%)

simplify66.0ms (1.1%)

prune100.0ms (1.7%)

localize20.0ms (0.3%)

rewrite39.0ms (0.7%)

series280.0ms (4.8%)

simplify93.0ms (1.6%)

prune109.0ms (1.9%)

localize16.0ms (0.3%)

rewrite46.0ms (0.8%)

series355.0ms (6.1%)

simplify74.0ms (1.3%)

prune144.0ms (2.5%)

localize17.0ms (0.3%)

rewrite56.0ms (1%)

series250.0ms (4.3%)

simplify101.0ms (1.7%)

prune112.0ms (1.9%)

regimes557.0ms (9.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (36.2%)

Profiling