Details

analyze389.0ms (14%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample24.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 40 to 20 computations (50% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`associate-r_binary64` `associate-+l+_binary64`
3×	`associate-+r+_binary64` `+-commutative_binary64`
2×	`distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate-l_binary64`
1×	`1-exp_binary64` `distribute-rgt-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	16	19
2	26	13
3	37	13
4	42	13
5	43	13
6	41	13

prune4.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 x y) (.f64 z (*.f64 z 3)))
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 72 to 40 computations (44.4% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x y) (.f64 z z))
0.0b	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

rewrite48.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip3-+_binary64` `*-un-lft-identity_binary64` `flip-+_binary64` `+-commutative_binary64`
2×	`associate-+l+_binary64`

Counts

3 → 38

Calls

3 calls:

9.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
6.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
4.0ms	(+.f64 (.f64 x y) (.f64 z z))

Compiler

Compiled 1009 to 149 computations (85.2% saved)

series123.0ms (4.4%)

Error

0.0b

Counts

3 → 54

Calls

3 calls:

42.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
38.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
31.0ms	(+.f64 (.f64 x y) (.f64 z z))

Compiler

Compiled 1200 to 757 computations (36.9% saved)

simplify95.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

548×	`associate--r+_binary64`
450×	`associate--l+_binary64`
387×	`distribute-rgt-in_binary64`
335×	`distribute-lft-in_binary64`
267×	`associate-l_binary64`

Counts

92 → 68

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	1316
1	225	1230
2	683	1115
3	2542	1115
4	4765	1115
5	4860	1115

prune34.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	4	70

Error

0.0b

Counts

70 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x y) (.f64 z (*.f64 z 3)))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
	39.0b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 x y) (.f64 2 (.f64 z z))) 3) (pow.f64 z 6)) (+.f64 (pow.f64 z 4) (.f64 (+.f64 (.f64 x y) (.f64 2 (.f64 z z))) (+.f64 (.f64 z z) (*.f64 x y)))))
	19.0b	(.f64 (sqrt.f64 (+.f64 (.f64 3 (.f64 z z)) (.f64 x y))) (sqrt.f64 (+.f64 (.f64 3 (.f64 z z)) (*.f64 x y))))

Compiler

Compiled 729 to 285 computations (60.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x y) (.f64 z (*.f64 z 3)))
0.2b	(.f64 z (.f64 z 3))

rewrite36.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `prod-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`
1×	`associate-r_binary64` `*-commutative_binary64` `sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64`

Counts

2 → 29

Calls

2 calls:

5.0ms	(.f64 z (.f64 z 3))
4.0ms	(+.f64 (.f64 x y) (.f64 z (*.f64 z 3)))

Compiler

Compiled 446 to 235 computations (47.3% saved)

series47.0ms (1.7%)

Error

0.0b

Counts

2 → 21

Calls

2 calls:

37.0ms	(+.f64 (.f64 x y) (.f64 z (*.f64 z 3)))
7.0ms	(.f64 z (.f64 z 3))

Compiler

Compiled 379 to 282 computations (25.6% saved)

simplify108.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-l_binary64`
526×	`unswap-sqr_binary64`
354×	`associate-r_binary64`
347×	`cancel-sign-sub-inv_binary64`
322×	`distribute-rgt-in_binary64`

Counts

50 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	598
1	170	568
2	562	547
3	1600	545
4	3528	545
5	4858	545
6	4996	545
7	4918	545

prune24.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	38	4	42

Error

0.0b

Counts

42 → 4

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (.f64 x y) (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (.f64 z z)))))
	29.2b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 9 (pow.f64 z 4))) (-.f64 (.f64 x y) (.f64 3 (*.f64 z z))))
✓	0.1b	(+.f64 (.f64 x y) (.f64 z (*.f64 z 3)))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 412 to 211 computations (48.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 z z))
0.3b	(.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z))))
19.5b	(sqrt.f64 (.f64 3 (.f64 z z)))
19.5b	(sqrt.f64 (.f64 3 (.f64 z z)))

rewrite120.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

148×	`pow1_binary64`
80×	`pow-prod-down_binary64`
66×	`sqrt-pow1_binary64`
17×	`pow-prod-up_binary64`
14×	`pow1/2_binary64`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z))))
5.0ms	(.f64 3 (.f64 z z))
5.0ms	(sqrt.f64 (.f64 3 (.f64 z z)))
4.0ms	(sqrt.f64 (.f64 3 (.f64 z z)))

Compiler

Compiled 1591 to 855 computations (46.3% saved)

series236.0ms (8.5%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

204.0ms	(.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (*.f64 z z))))
8.0ms	(sqrt.f64 (.f64 3 (.f64 z z)))
8.0ms	(sqrt.f64 (.f64 3 (.f64 z z)))
8.0ms	(.f64 3 (.f64 z z))

Compiler

Compiled 530 to 385 computations (27.4% saved)

simplify89.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

585×	`associate-*l/_binary64`
519×	`associate-r_binary64`
450×	`*-commutative_binary64`
305×	`associate-/l*_binary64`
295×	`sqr-pow_binary64`

Counts

121 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	1061
1	134	907
2	403	878
3	981	865
4	1826	766
5	2570	766
6	4953	766

prune43.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	91	4	95

Error

0.0b

Counts

95 → 4

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (.f64 x y) (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (.f64 z z)))))
✓	0.1b	(+.f64 (.f64 x y) (.f64 z (*.f64 z 3)))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
▶	13.4b	(+.f64 (.f64 x y) (sqrt.f64 (.f64 9 (pow.f64 z 4))))

Compiler

Compiled 695 to 393 computations (43.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x y) (sqrt.f64 (.f64 9 (pow.f64 z 4))))
0.1b	(*.f64 9 (pow.f64 z 4))
18.5b	(sqrt.f64 (*.f64 9 (pow.f64 z 4)))

rewrite64.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
5×	`add-log-exp_binary64` `add-cbrt-cube_binary64`

Counts

3 → 46

Calls

3 calls:

5.0ms	(*.f64 9 (pow.f64 z 4))
4.0ms	(+.f64 (.f64 x y) (sqrt.f64 (.f64 9 (pow.f64 z 4))))
3.0ms	(sqrt.f64 (*.f64 9 (pow.f64 z 4)))

Compiler

Compiled 780 to 537 computations (31.2% saved)

series56.0ms (2%)

Error

0.0b

Counts

3 → 24

Calls

3 calls:

37.0ms	(+.f64 (.f64 x y) (sqrt.f64 (.f64 9 (pow.f64 z 4))))
9.0ms	(*.f64 9 (pow.f64 z 4))
7.0ms	(sqrt.f64 (*.f64 9 (pow.f64 z 4)))

Compiler

Compiled 467 to 348 computations (25.5% saved)

simplify132.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

524×	`distribute-rgt-in_binary64`
441×	`distribute-lft-in_binary64`
435×	`*-commutative_binary64`
312×	`associate-l_binary64`
240×	`associate-r_binary64`

Counts

70 → 38

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	833
1	186	790
2	447	776
3	1237	776
4	2323	770
5	4517	770
6	4822	770
7	4988	770
8	4911	770

prune21.0ms (0.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	38	4	42

Error

0.0b

Counts

42 → 4

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 x y) (.f64 (sqrt.f64 (.f64 3 (.f64 z z))) (sqrt.f64 (.f64 3 (.f64 z z)))))
	0.1b	(+.f64 (.f64 x y) (.f64 z (*.f64 z 3)))
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
	13.4b	(+.f64 (.f64 x y) (sqrt.f64 (.f64 9 (pow.f64 z 4))))

Compiler

Compiled 322 to 196 computations (39.1% saved)

regimes422.0ms (15.1%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Compiler

Compiled 6735 to 3717 computations (44.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	15	19
2	15	19

end7.0ms (0.2%)

Remove: (sort x y)
Compiler: Compiled 48 to 33 computations (31.3% saved)

sample618.0ms (22.2%)

Algorithm

1×

intervals

Results

249.0ms	8000×	body	128	valid
13.0ms	472×	body	128	invalid

Compiler

Compiled 101 to 62 computations (38.6% saved)

Details

analyze389.0ms (14%)

sample24.0ms (0.8%)

simplify9.0ms (0.3%)

prune4.0ms (0.2%)

localize11.0ms (0.4%)

rewrite48.0ms (1.7%)

series123.0ms (4.4%)

simplify95.0ms (3.4%)

prune34.0ms (1.2%)

localize6.0ms (0.2%)

rewrite36.0ms (1.3%)

series47.0ms (1.7%)

simplify108.0ms (3.9%)

prune24.0ms (0.9%)

localize9.0ms (0.3%)

rewrite120.0ms (4.3%)

series236.0ms (8.5%)

simplify89.0ms (3.2%)

prune43.0ms (1.5%)

localize8.0ms (0.3%)

rewrite64.0ms (2.3%)

series56.0ms (2%)

simplify132.0ms (4.8%)

prune21.0ms (0.7%)

regimes422.0ms (15.1%)

simplify3.0ms (0.1%)

end7.0ms (0.2%)

sample618.0ms (22.2%)

Profiling