Details

analyze329.0ms (7.2%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
18×	`associate-/r*_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	16
2	38	16
3	87	16
4	108	16
5	118	16
6	111	16

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

9.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	9.1b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

4.8b	(.f64 y (+.f64 1 (.f64 z z)))
5.5b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

rewrite120.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 74

Calls

2 calls:

10.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))

Compiler

Compiled 1356 to 790 computations (41.7% saved)

series79.0ms (1.7%)

Error

6.6b

Counts

2 → 19

Calls

2 calls:

44.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
24.0ms	(.f64 y (+.f64 1 (.f64 z z)))

Compiler

Compiled 583 to 422 computations (27.6% saved)

simplify124.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

416×	`associate-/r*_binary64`
399×	`associate-r_binary64`
379×	`associate-/l*_binary64`
318×	`associate-+l+_binary64`
309×	`associate-/l/_binary64`

Counts

93 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1707
1	309	1434
2	985	1432
3	3170	1432
4	4555	1432
5	4965	1432
6	4964	1432

prune64.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	70	9	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	9	80

Error

6.6b

Counts

80 → 9

Alt Table

Status	Error	Program
▶	7.5b	(.f64 (/.f64 1 y) (/.f64 1 (+.f64 x (.f64 x (*.f64 z z)))))
	27.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))) 3)))
	49.6b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 x)) y) (/.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 1 (.f64 z z))))
	9.1b	(/.f64 1 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))))
	25.6b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 y (.f64 (.f64 z z) y))) (sqrt.f64 (+.f64 y (.f64 (*.f64 z z) y)))))
	8.3b	(/.f64 (/.f64 1 (.f64 x y)) (+.f64 1 (.f64 z z)))
	9.6b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (.f64 z z) y))))) (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (.f64 z z) y)))))) (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))))))
	9.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (+.f64 y (.f64 (.f64 z z) y)) (cbrt.f64 x)))
	8.7b	(/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 y (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (.f64 z z)))))

Compiler

Compiled 1072 to 515 computations (52% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 x (.f64 z z)))
0.3b	(/.f64 1 (+.f64 x (.f64 x (.f64 z z))))
3.8b	(.f64 (/.f64 1 y) (/.f64 1 (+.f64 x (.f64 x (*.f64 z z)))))
8.2b	(.f64 x (.f64 z z))

rewrite186.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

53×	`add-exp-log_binary64`
52×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`

Counts

4 → 135

Calls

4 calls:

14.0ms	(.f64 (/.f64 1 y) (/.f64 1 (+.f64 x (.f64 x (*.f64 z z)))))
6.0ms	(.f64 x (.f64 z z))
5.0ms	(/.f64 1 (+.f64 x (.f64 x (.f64 z z))))
3.0ms	(+.f64 x (.f64 x (.f64 z z)))

Compiler

Compiled 2873 to 1166 computations (59.4% saved)

series115.0ms (2.5%)

Error

6.6b

Counts

4 → 32

Calls

4 calls:

43.0ms	(.f64 (/.f64 1 y) (/.f64 1 (+.f64 x (.f64 x (*.f64 z z)))))
24.0ms	(/.f64 1 (+.f64 x (.f64 x (.f64 z z))))
20.0ms	(+.f64 x (.f64 x (.f64 z z)))
17.0ms	(.f64 x (.f64 z z))

Compiler

Compiled 1042 to 779 computations (25.2% saved)

simplify144.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

367×	`times-frac_binary64`
315×	`distribute-rgt-in_binary64`
293×	`distribute-lft-in_binary64`
211×	`*-commutative_binary64`
193×	`associate-/l*_binary64`

Counts

167 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	3034
1	374	2693
2	912	2679
3	2626	2679
4	4642	2679
5	4980	2679

prune292.0ms (6.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	128	10	138

Error

5.7b

Counts

138 → 10

Alt Table

Status	Error	Program
	48.7b	(.f64 (/.f64 1 y) (/.f64 1 (+.f64 x (.f64 (sqrt.f64 x) (.f64 z (.f64 z (sqrt.f64 x)))))))
	27.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))) 3)))
	9.1b	(/.f64 1 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))))
	25.6b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 y (.f64 (.f64 z z) y))) (sqrt.f64 (+.f64 y (.f64 (*.f64 z z) y)))))
	8.3b	(/.f64 (/.f64 1 (.f64 x y)) (+.f64 1 (.f64 z z)))
	9.6b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (.f64 z z) y))))) (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (.f64 z z) y)))))) (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))))))
	23.9b	(.f64 (/.f64 1 y) (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x (.f64 x (*.f64 z z)))) 3)))
	7.5b	(.f64 (/.f64 1 y) (pow.f64 (+.f64 x (.f64 x (*.f64 z z))) -1))
▶	7.4b	(/.f64 1 (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))
	8.0b	(.f64 (/.f64 (/.f64 1 y) (.f64 (cbrt.f64 (+.f64 x (.f64 x (.f64 z z)))) (cbrt.f64 (+.f64 x (.f64 x (.f64 z z)))))) (/.f64 1 (cbrt.f64 (+.f64 x (.f64 x (.f64 z z))))))

Compiler

Compiled 1646 to 723 computations (56.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 x (.f64 z z)))
0.4b	(/.f64 1 (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))
3.8b	(.f64 y (+.f64 x (.f64 x (*.f64 z z))))
8.2b	(.f64 x (.f64 z z))

rewrite115.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

22×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
14×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(/.f64 1 (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))
6.0ms	(.f64 x (.f64 z z))
6.0ms	(.f64 y (+.f64 x (.f64 x (*.f64 z z))))
3.0ms	(+.f64 x (.f64 x (.f64 z z)))

Compiler

Compiled 1414 to 417 computations (70.5% saved)

series131.0ms (2.9%)

Error

5.7b

Counts

4 → 37

Calls

4 calls:

46.0ms	(/.f64 1 (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))
38.0ms	(.f64 y (+.f64 x (.f64 x (*.f64 z z))))
20.0ms	(+.f64 x (.f64 x (.f64 z z)))
15.0ms	(.f64 x (.f64 z z))

Compiler

Compiled 1062 to 759 computations (28.5% saved)

simplify119.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

553×	`times-frac_binary64`
319×	`distribute-rgt-in_binary64`
301×	`distribute-lft-in_binary64`
286×	`*-commutative_binary64`
226×	`associate-/r*_binary64`

Counts

119 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1770
1	299	1566
2	1070	1554
3	3591	1552
4	4658	1552
5	4960	1552

prune47.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Error

5.6b

Counts

87 → 9

Alt Table

Status	Error	Program
	48.7b	(/.f64 1 (.f64 y (+.f64 x (.f64 (sqrt.f64 x) (.f64 z (.f64 z (sqrt.f64 x)))))))
	27.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))) 3)))
	9.1b	(/.f64 1 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))))
	25.6b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 y (.f64 (.f64 z z) y))) (sqrt.f64 (+.f64 y (.f64 (*.f64 z z) y)))))
	8.3b	(/.f64 (/.f64 1 (.f64 x y)) (+.f64 1 (.f64 z z)))
	9.6b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (.f64 z z) y))))) (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (.f64 z z) y)))))) (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))))))
	24.0b	(/.f64 1 (.f64 y (cbrt.f64 (pow.f64 (+.f64 x (.f64 x (*.f64 z z))) 3))))
	7.5b	(.f64 (/.f64 1 y) (pow.f64 (+.f64 x (.f64 x (*.f64 z z))) -1))
▶	7.4b	(/.f64 (sqrt.f64 1) (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))

Compiler

Compiled 824 to 400 computations (51.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 x (.f64 z z)))
0.4b	(/.f64 (sqrt.f64 1) (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))
3.8b	(.f64 y (+.f64 x (.f64 x (*.f64 z z))))
8.2b	(.f64 x (.f64 z z))

rewrite125.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `times-frac_binary64` `sqrt-prod_binary64` `associate-/l*_binary64`
5×	`prod-exp_binary64` `cbrt-unprod_binary64`

Counts

4 → 81

Calls

4 calls:

7.0ms	(/.f64 (sqrt.f64 1) (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))
6.0ms	(.f64 x (.f64 z z))
6.0ms	(.f64 y (+.f64 x (.f64 x (*.f64 z z))))
3.0ms	(+.f64 x (.f64 x (.f64 z z)))

Compiler

Compiled 1506 to 526 computations (65.1% saved)

series140.0ms (3%)

Error

5.6b

Counts

4 → 37

Calls

4 calls:

45.0ms	(/.f64 (sqrt.f64 1) (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))
39.0ms	(.f64 y (+.f64 x (.f64 x (*.f64 z z))))
22.0ms	(+.f64 x (.f64 x (.f64 z z)))
16.0ms	(.f64 x (.f64 z z))

Compiler

Compiled 1167 to 847 computations (27.4% saved)

simplify125.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

553×	`times-frac_binary64`
317×	`distribute-rgt-in_binary64`
301×	`distribute-lft-in_binary64`
284×	`*-commutative_binary64`
226×	`associate-/r*_binary64`

Counts

118 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	1790
1	295	1586
2	1063	1574
3	3591	1572
4	4658	1572
5	4966	1572

prune45.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Error

5.6b

Counts

92 → 9

Alt Table

Status	Error	Program
	48.7b	(/.f64 1 (.f64 y (+.f64 x (.f64 (sqrt.f64 x) (.f64 z (.f64 z (sqrt.f64 x)))))))
	27.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))) 3)))
	9.1b	(/.f64 1 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))))
	25.6b	(/.f64 (/.f64 1 x) (.f64 (sqrt.f64 (+.f64 y (.f64 (.f64 z z) y))) (sqrt.f64 (+.f64 y (.f64 (*.f64 z z) y)))))
	8.3b	(/.f64 (/.f64 1 (.f64 x y)) (+.f64 1 (.f64 z z)))
	9.6b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (.f64 z z) y))))) (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (.f64 z z) y)))))) (cbrt.f64 (/.f64 1 (.f64 x (+.f64 y (.f64 (*.f64 z z) y))))))
	24.0b	(/.f64 1 (.f64 y (cbrt.f64 (pow.f64 (+.f64 x (.f64 x (*.f64 z z))) 3))))
	7.5b	(.f64 (/.f64 1 y) (pow.f64 (+.f64 x (.f64 x (*.f64 z z))) -1))
	7.4b	(/.f64 (sqrt.f64 1) (.f64 y (+.f64 x (.f64 x (*.f64 z z)))))

Compiler

Compiled 782 to 352 computations (55% saved)

regimes1.5s (32%)

Accuracy

Total -0.3b remaining (-6.9%)

Threshold costs -0.3b (-6.9%)

Compiler

Compiled 26021 to 16531 computations (36.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	15	16

end6.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 42 to 27 computations (35.7% saved)

sample743.0ms (16.2%)

Algorithm

1×

intervals

Results

292.0ms	8000×	body	128	valid
15.0ms	445×	body	128	invalid

Compiler

Compiled 208 to 127 computations (38.9% saved)

Details

analyze329.0ms (7.2%)

sample25.0ms (0.5%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite120.0ms (2.6%)

series79.0ms (1.7%)

simplify124.0ms (2.7%)

prune64.0ms (1.4%)

localize11.0ms (0.2%)

rewrite186.0ms (4%)

series115.0ms (2.5%)

simplify144.0ms (3.1%)

prune292.0ms (6.3%)

localize8.0ms (0.2%)

rewrite115.0ms (2.5%)

series131.0ms (2.9%)

simplify119.0ms (2.6%)

prune47.0ms (1%)

localize8.0ms (0.2%)

rewrite125.0ms (2.7%)

series140.0ms (3%)

simplify125.0ms (2.7%)

prune45.0ms (1%)

regimes1.5s (32%)

simplify3.0ms (0.1%)

end6.0ms (0.1%)

sample743.0ms (16.2%)

Profiling