Details

analyze768.0ms (14%)

Algorithm

1×

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)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	200×	body	128	valid
7.0ms	256×	pre	128	true
6.0ms	25×	body	2048	valid
2.0ms	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)

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (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)

localize12.0ms (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)))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_1481` `pow1_binary64_1503`
7×	`*-un-lft-identity_binary64_1442`
6×	`add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477`
4×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-exp-log_binary64_1480` `sqrt-prod_binary64_1458` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`sqrt-pow1_binary64_1460`
2×	`associate-*r/_binary64_1384` `sum-log_binary64_1533` `+-commutative_binary64_1372` `pow1/2_binary64_1522`
1×	`rem-sqrt-square_binary64_1455` `pow-prod-down_binary64_1513` `distribute-lft-out_binary64_1393`

Counts

4 → 51

Calls

4 calls:

16.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.0ms	(sqrt.f64 (.f64 1/2 (+.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)))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

series187.0ms (3.4%)

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)))))))
41.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
24.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
21.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4937	1285
1	4937	1285

prune95.0ms (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)

localize15.0ms (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)))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64_1503` `*-un-lft-identity_binary64_1442`
8×	`add-sqr-sqrt_binary64_1464`
7×	`add-cube-cbrt_binary64_1477`
6×	`add-log-exp_binary64_1481`
5×	`log-pow_binary64_1531` `sqrt-prod_binary64_1458`
4×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-exp-log_binary64_1480` `exp-prod_binary64_1494`
3×	`sqrt-pow1_binary64_1460` `log-prod_binary64_1528` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-*r/_binary64_1384` `pow1/2_binary64_1522`
1×	`rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `rem-log-exp_binary64_1483` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `distribute-lft-out_binary64_1393`

Counts

4 → 56

Calls

4 calls:

17.0ms	(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)))))))))

series286.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
97.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
41.0ms	(+.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)))

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4893	1559
1	4893	1559

prune110.0ms (2%)

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)

localize17.0ms (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)))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-prod_binary64_1473`
13×	`*-un-lft-identity_binary64_1442`
12×	`add-sqr-sqrt_binary64_1464`
11×	`add-cube-cbrt_binary64_1477`
9×	`pow1_binary64_1503`
8×	`cube-prod_binary64_1470` `unpow-prod-down_binary64_1521`
7×	`sqrt-prod_binary64_1458`
6×	`sqrt-div_binary64_1459` `add-log-exp_binary64_1481`
5×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
4×	`associate-*r/_binary64_1384` `flip3-+_binary64_1445` `flip-+_binary64_1416` `cube-div_binary64_1471` `pow-pow_binary64_1514`
3×	`sqrt-pow1_binary64_1460` `pow-unpow_binary64_1519`
2×	`cube-mult_binary64_1472` `cbrt-div_binary64_1474` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `pow1/2_binary64_1522`
1×	`rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `pow-exp_binary64_1510` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `rem-cube-cbrt_binary64_1465` `distribute-lft-out_binary64_1393` `pow1/3_binary64_1524` `sqrt-pow2_binary64_1461` `pow-to-exp_binary64_1511` `rem-cbrt-cube_binary64_1466`

Counts

4 → 83

Calls

4 calls:

17.0ms	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))) 3)
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)))
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))

series370.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))) 3)
107.0ms	(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))
45.0ms	(+.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)))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	2595
1	4962	2595

prune144.0ms (2.6%)

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)

localize13.0ms (0.2%)

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)))

rewrite59.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1464`
18×	`sqrt-prod_binary64_1458`
16×	`*-un-lft-identity_binary64_1442`
10×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
7×	`associate-r_binary64_1382`
6×	`add-cbrt-cube_binary64_1478` `associate-l_binary64_1383` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
4×	`sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `unswap-sqr_binary64_1410`
3×	`pow-prod-down_binary64_1513` `distribute-lft-out_binary64_1393`
2×	`associate-*r/_binary64_1384` `rem-sqrt-square_binary64_1455`
1×	`cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `sqrt-unprod_binary64_1462` `prod-exp_binary64_1491`

Counts

4 → 76

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
13.0ms	(sqrt.f64 (+.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)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series243.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
74.0ms	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
41.0ms	(+.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)))

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5113	2192

prune105.0ms (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)

regimes517.0ms (9.4%)

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%)

sample1.9s (35.4%)

Algorithm

1×

intervals

Results

317.0ms	6114×	body	128	valid
203.0ms	784×	body	2048	valid
145.0ms	8000×	pre	128	true
109.0ms	524×	body	1024	valid
76.0ms	234×	body	4096	valid
38.0ms	225×	body	512	valid
12.0ms	119×	body	256	valid

Compiler

Compiled 912 to 740 computations (18.9% saved)

Details

analyze768.0ms (14%)

sample39.0ms (0.7%)

simplify97.0ms (1.8%)

prune3.0ms (0.1%)

localize12.0ms (0.2%)

rewrite46.0ms (0.8%)

series187.0ms (3.4%)

simplify64.0ms (1.2%)

prune95.0ms (1.7%)

localize15.0ms (0.3%)

rewrite42.0ms (0.8%)

series286.0ms (5.2%)

simplify89.0ms (1.6%)

prune110.0ms (2%)

localize17.0ms (0.3%)

rewrite47.0ms (0.9%)

series370.0ms (6.8%)

simplify75.0ms (1.4%)

prune144.0ms (2.6%)

localize13.0ms (0.2%)

rewrite59.0ms (1.1%)

series243.0ms (4.4%)

simplify97.0ms (1.8%)

prune105.0ms (1.9%)

regimes517.0ms (9.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (35.4%)

Profiling