Details

analyze1.1s (25.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
25%	74.9%	0.2%	7
25%	74.9%	0.2%	8
34.3%	65.5%	0.2%	9
39%	60.8%	0.2%	10
48.3%	51.5%	0.2%	11
53.7%	46.1%	0.2%	12
63.1%	36.7%	0.2%	13
64%	35.6%	0.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	15×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify17.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

28×	`cancel-sign-sub-inv_binary64`
21×	`sub-neg_binary64`
13×	`neg-mul-1_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-rgt-in_binary64`
11×	`unsub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

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

2.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 y (*.f64 z t))
2.9b	(/.f64 x (-.f64 y (*.f64 z t)))

rewrite49.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
4×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l_binary64` `associate-/r_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
3.0ms	(-.f64 y (*.f64 z t))

Compiler

Compiled 631 to 143 computations (77.3% saved)

series76.0ms (1.8%)

Error

2.9b

Counts

2 → 38

Calls

2 calls:

49.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
22.0ms	(-.f64 y (*.f64 z t))

Compiler

Compiled 980 to 649 computations (33.8% saved)

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

497×	`associate-*l/_binary64`
478×	`associate-/r/_binary64`
285×	`distribute-rgt-in_binary64`
239×	`distribute-lft-in_binary64`
227×	`unswap-sqr_binary64`

Counts

79 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1142
1	218	1085
2	607	1083
3	2113	1035
4	5034	1035

prune40.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	50	5	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	6	56

Error

2.7b

Counts

56 → 6

Alt Table

Status	Error	Program
	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 t z)))))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	3.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
▶	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	28.5b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))

Compiler

Compiled 747 to 238 computations (68.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 y (*.f64 t z))
0.3b	(/.f64 1 (-.f64 y (*.f64 t z)))
2.9b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))

rewrite88.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

26×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `times-frac_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
15×	`associate-r_binary64`

Counts

3 → 83

Calls

3 calls:

10.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
4.0ms	(/.f64 1 (-.f64 y (*.f64 t z)))
3.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1405 to 540 computations (61.6% saved)

series120.0ms (2.8%)

Error

2.7b

Counts

3 → 55

Calls

3 calls:

49.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
35.0ms	(/.f64 1 (-.f64 y (*.f64 t z)))
27.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1644 to 1137 computations (30.8% saved)

simplify127.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
414×	`times-frac_binary64`
367×	`associate-/l*_binary64`
321×	`associate-l_binary64`
286×	`unswap-sqr_binary64`

Counts

138 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1997
1	297	1859
2	941	1833
3	3209	1833
4	4599	1833
5	5606	1833

prune35.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	75	6	81

Error

2.7b

Counts

81 → 6

Alt Table

Status	Error	Program
	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 t z)))))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
▶	3.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	28.5b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))

Compiler

Compiled 755 to 282 computations (62.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 y (*.f64 t z))
1.0b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
2.5b	(/.f64 (-.f64 y (*.f64 t z)) x)

rewrite126.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

84×	`times-frac_binary64`
53×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
16×	`add-exp-log_binary64` `associate-/r*_binary64`
10×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`

Counts

3 → 118

Calls

3 calls:

10.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
5.0ms	(/.f64 (-.f64 y (*.f64 t z)) x)
3.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 2282 to 715 computations (68.7% saved)

series129.0ms (3%)

Error

2.7b

Counts

3 → 59

Calls

3 calls:

49.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
48.0ms	(/.f64 (-.f64 y (*.f64 t z)) x)
24.0ms	(-.f64 y (*.f64 t z))

Compiler

Compiled 1534 to 1041 computations (32.1% saved)

simplify166.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

523×	`times-frac_binary64`
419×	`associate-l_binary64`
412×	`associate-/l*_binary64`
319×	`associate-/r/_binary64`
307×	`associate-*l/_binary64`

Counts

177 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	3191
1	406	2951
2	1331	2933
3	4310	2933
4	4989	2933
5	4971	2933

prune50.0ms (1.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	109	6	115

Error

2.7b

Counts

115 → 6

Alt Table

Status	Error	Program
▶	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 t z)))))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	3.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	28.5b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))

Compiler

Compiled 1098 to 347 computations (68.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
7.1b	(cbrt.f64 (-.f64 y (*.f64 t z)))
7.1b	(cbrt.f64 (-.f64 y (*.f64 t z)))
7.1b	(cbrt.f64 (-.f64 y (*.f64 t z)))

rewrite92.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

18×	`cbrt-div_binary64`
15×	`add-exp-log_binary64`
12×	`pow1_binary64`
9×	`pow1/3_binary64` `add-cube-cbrt_binary64` `flip3--_binary64` `flip--_binary64` `cbrt-prod_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `pow-flip_binary64`
8×	`associate-/r/_binary64`

Counts

4 → 82

Calls

4 calls:

10.0ms	(/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
2.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))

Compiler

Compiled 2583 to 510 computations (80.3% saved)

series277.0ms (6.5%)

Error

2.7b

Counts

4 → 62

Calls

4 calls:

64.0ms	(/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (*.f64 t z)))))
58.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
57.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))
57.0ms	(cbrt.f64 (-.f64 y (*.f64 t z)))

Compiler

Compiled 5843 to 3664 computations (37.3% saved)

simplify151.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

530×	`associate-r_binary64`
491×	`associate-l_binary64`
222×	`times-frac_binary64`
205×	`associate-/l*_binary64`
201×	`associate-/r*_binary64`

Counts

144 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	2939
1	490	2721
2	1292	2645
3	4749	2602
4	4977	2602
5	4957	2602

prune62.0ms (1.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	100	6	106

Error

2.7b

Counts

106 → 6

Alt Table

Status	Error	Program
	3.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 t z)))))
	3.7b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	3.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 t z)) x))
	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 t z))))
	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	28.5b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 t z)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 t z)))))

Compiler

Compiled 2075 to 709 computations (65.8% saved)

regimes841.0ms (19.6%)

Accuracy

Total 0.1b remaining (2.1%)

Threshold costs 0.1b (2.1%)

Compiler

Compiled 10594 to 5787 computations (45.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`sub-neg_binary64` `*-commutative_binary64` `+-commutative_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`distribute-lft-neg-out_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	30	10
4	34	10
5	35	10
6	35	10

end6.0ms (0.1%)

Remove: (sort z t)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample631.0ms (14.7%)

Algorithm

1×

intervals

Results

228.0ms	8000×	body	128	valid
9.0ms	343×	body	128	invalid

Compiler

Compiled 131 to 75 computations (42.7% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10

Details

analyze1.1s (25.3%)

sample24.0ms (0.6%)

simplify17.0ms (0.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite49.0ms (1.1%)

series76.0ms (1.8%)

simplify67.0ms (1.6%)

prune40.0ms (0.9%)

localize7.0ms (0.2%)

rewrite88.0ms (2%)

series120.0ms (2.8%)

simplify127.0ms (2.9%)

prune35.0ms (0.8%)

localize7.0ms (0.2%)

rewrite126.0ms (2.9%)

series129.0ms (3%)

simplify166.0ms (3.9%)

prune50.0ms (1.2%)

localize12.0ms (0.3%)

rewrite92.0ms (2.1%)

series277.0ms (6.5%)

simplify151.0ms (3.5%)

prune62.0ms (1.5%)

regimes841.0ms (19.6%)

simplify3.0ms (0.1%)

end6.0ms (0.1%)

sample631.0ms (14.7%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	36	10
4	47	10
5	67	10
6	92	10
7	113	10
8	144	10
9	154	10
10	149	10
11	126	10