Details

analyze768.0ms (12.9%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	192×	body	128	valid
6.0ms	25×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	10×	body	4096	valid
3.0ms	15×	body	1024	valid
2.0ms	11×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	37	26
1	37	26

prune3.0ms (0%)

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

Merged error: 14.0b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.5b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.1b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
16×	`sqrt-prod_binary64`
8×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`sqrt-pow1_binary64` `associate-/l*_binary64`
2×	`pow1/2_binary64` `associate-*r/_binary64` `associate-/r/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 81

Calls

4 calls:

15.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
15.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
9.0ms	(/.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)))

series392.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
87.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
58.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
45.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4986	2228
1	4986	2228

prune549.0ms (9.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	12	94

Merged error: 13.7b

Counts

94 → 12

Compiler

Compiled 11015 to 7936 computations (28% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.1b	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
4.6b	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
14.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite74.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
24×	`cancel-sign-sub-inv_binary64`
21×	`add-cube-cbrt_binary64`
18×	`sqrt-prod_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
3×	`associate-/r*_binary64` `distribute-rgt-out--_binary64`
2×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 99

Calls

4 calls:

33.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
12.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series252.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
62.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
48.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
48.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5169	3013

prune315.0ms (5.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	110	13	123

Merged error: 13.7b

Counts

123 → 13

Compiler

Compiled 6941 to 4264 computations (38.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
2.2b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
14.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`
24×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `sqrt-div_binary64`
5×	`unswap-sqr_binary64`
4×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
3×	`associate-l_binary64` `prod-exp_binary64` `associate-/l*_binary64` `pow-flip_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 120

Calls

4 calls:

19.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
9.0ms	(/.f64 1 (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	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))

series252.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
64.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
59.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
47.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify110.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5122	2849

prune435.0ms (7.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	5	5	10
Picked	1	0	1
Done	0	2	2
Total	133	12	145

Merged error: 13.7b

Counts

145 → 12

Compiler

Compiled 8896 to 6249 computations (29.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.2b	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
2.2b	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))
14.1b	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
3×	`pow-unpow_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`
1×	`cbrt-unprod_binary64` `pow-pow_binary64` `*-commutative_binary64`

Counts

4 → 64

Calls

4 calls:

11.0ms	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
8.0ms	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)
6.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
4.0ms	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))

series336.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(pow.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)) -1/2)
80.0ms	(+.f64 1 (.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2)))
58.0ms	(.f64 x (pow.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)) -1/2))
42.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5507	1565

prune246.0ms (4.1%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	74	14	88

Merged error: 13.7b

Counts

88 → 14

Compiler

Compiled 5231 to 3682 computations (29.6% saved)

regimes253.0ms (4.2%)

Compiler: Compiled 3625 to 2625 computations (27.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	20	26

end0.0ms (0%)

sample1.5s (24.8%)

Algorithm

1×

intervals

Results

301.0ms	6079×	body	128	valid
199.0ms	786×	body	2048	valid
149.0ms	8000×	pre	128	true
94.0ms	487×	body	1024	valid
89.0ms	274×	body	4096	valid
37.0ms	261×	body	512	valid
11.0ms	113×	body	256	valid

Compiler

Compiled 552 to 406 computations (26.4% saved)

Details

analyze768.0ms (12.9%)

sample38.0ms (0.6%)

simplify12.0ms (0.2%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite53.0ms (0.9%)

series392.0ms (6.6%)

simplify98.0ms (1.7%)

prune549.0ms (9.2%)

localize18.0ms (0.3%)

rewrite74.0ms (1.2%)

series252.0ms (4.2%)

simplify75.0ms (1.3%)

prune315.0ms (5.3%)

localize12.0ms (0.2%)

rewrite51.0ms (0.9%)

series252.0ms (4.2%)

simplify110.0ms (1.8%)

prune435.0ms (7.3%)

localize16.0ms (0.3%)

rewrite35.0ms (0.6%)

series336.0ms (5.6%)

simplify71.0ms (1.2%)

prune246.0ms (4.1%)

regimes253.0ms (4.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (24.8%)

Profiling