Details

analyze1.1s (29.6%)

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
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.2s (30.7%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
504×	`associate-*l/_binary64`
466×	`div-sub_binary64`
450×	`cancel-sign-sub-inv_binary64`
403×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	30	25
2	70	25
3	177	22
4	486	19
5	1087	19
6	2534	19
7	4434	19
8	5156	19

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

3.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.5b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	11.3b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))
✓	3.4b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	6.0b	(/.f64 (.f64 y t) (.f64 2 z))

series52.0ms (1.4%)

Counts

3 → 108

Calls

3 calls:

27.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
14.0ms	(/.f64 (.f64 y t) (.f64 2 z))
11.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 100

Calls

3 calls:

6.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(/.f64 (.f64 y t) (.f64 2 z))
4.0ms	(-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))

simplify167.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-def_binary64`
250×	`cancel-sign-sub-inv_binary64`
249×	`distribute-rgt-neg-in_binary64`
238×	`exp-prod_binary64`
226×	`times-frac_binary64`

Counts

208 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	4237
1	562	3982
2	2311	3590
3	4379	3590
4	4991	3590
5	4989	3590
6	4835	3590

prune135.0ms (3.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	171	3	174

Error

0.0b

Counts

174 → 3

Alt Table

Status	Error	Program
▶	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	11.3b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	25.7b	(-.f64 x (*.f64 -2 (/.f64 z t)))

Compiler

Compiled 4377 to 2165 computations (50.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))
✓	3.4b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
✓	3.9b	(*.f64 (/.f64 y 2) (/.f64 t z))

series59.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

29.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
19.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
11.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 103

Calls

3 calls:

8.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
4.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
3.0ms	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))

simplify95.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

771×	`associate-/r*_binary64`
401×	`associate-/l/_binary64`
302×	`fma-def_binary64`
274×	`associate-/r/_binary64`
155×	`associate-*l/_binary64`

Counts

211 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	3950
1	628	3813
2	2088	3593
3	5402	3593

prune144.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	181	5	186

Error

Counts

186 → 5

Alt Table

Status	Error	Program
▶	1.0b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 (/.f64 y 2) (/.f64 t z))))))
✓	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	11.3b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	25.7b	(-.f64 x (*.f64 -2 (/.f64 z t)))
	35.0b	(-.f64 x (/.f64 (sqrt.f64 y) (/.f64 (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))) (sqrt.f64 y))))

Compiler

Compiled 4163 to 2057 computations (50.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))
✓	0.1b	(/.f64 1 (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
✓	3.4b	(.f64 y (/.f64 1 (-.f64 z (.f64 (/.f64 y 2) (/.f64 t z)))))
	3.9b	(*.f64 (/.f64 y 2) (/.f64 t z))

series59.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

30.0ms	(.f64 y (/.f64 1 (-.f64 z (.f64 (/.f64 y 2) (/.f64 t z)))))
29.0ms	(/.f64 1 (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 75

Calls

2 calls:

7.0ms	(.f64 y (/.f64 1 (-.f64 z (.f64 (/.f64 y 2) (/.f64 t z)))))
3.0ms	(/.f64 1 (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

simplify90.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

795×	`associate-/l*_binary64`
690×	`associate-/r*_binary64`
338×	`fma-def_binary64`
171×	`associate-/r/_binary64`
118×	`associate-/l/_binary64`

Counts

147 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	4147
1	452	3956
2	1691	3911
3	5040	3911

prune219.0ms (5.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	257	5	262

Error

Counts

262 → 5

Alt Table

Status	Error	Program
✓	1.0b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 (/.f64 y 2) (/.f64 t z))))))
✓	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
▶	11.3b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	25.7b	(-.f64 x (*.f64 -2 (/.f64 z t)))
	35.0b	(-.f64 x (/.f64 (sqrt.f64 y) (/.f64 (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))) (sqrt.f64 y))))

Compiler

Compiled 6518 to 3655 computations (43.9% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.1b	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))
✓	19.3b	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))

series48.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

34.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
13.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

7.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))
4.0ms	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

686×	`associate-/r*_binary64`
481×	`associate-/l/_binary64`
310×	`associate-/r/_binary64`
310×	`fma-def_binary64`
146×	`associate-l_binary64`

Counts

115 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	2819
1	441	2585
2	1881	2498
3	4975	2498

prune75.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	92	5	97

Error

Counts

97 → 5

Alt Table

Status	Error	Program
✓	1.0b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (.f64 (/.f64 y 2) (/.f64 t z))))))
✓	1.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	11.3b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
	25.7b	(-.f64 x (*.f64 -2 (/.f64 z t)))
	35.0b	(-.f64 x (/.f64 (sqrt.f64 y) (/.f64 (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))) (sqrt.f64 y))))

Compiler

Compiled 2516 to 1404 computations (44.2% saved)

regimes71.0ms (1.9%)

Accuracy

Total 1.1b remaining (99.6%)

Threshold costs 0b (0%)

Counts

10 → 1

Compiler

Compiled 1110 to 740 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	20	19
2	36	19
3	48	19
4	57	19
5	61	19
6	62	19
7	62	19

end70.0ms (1.8%)

Compiler: Compiled 123 to 81 computations (34.1% saved)

Details

analyze1.1s (29.6%)

sample1.2s (30.7%)

simplify53.0ms (1.4%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series52.0ms (1.4%)

rewrite20.0ms (0.5%)

simplify167.0ms (4.4%)

prune135.0ms (3.5%)

localize8.0ms (0.2%)

series59.0ms (1.5%)

rewrite20.0ms (0.5%)

simplify95.0ms (2.5%)

prune144.0ms (3.7%)

localize10.0ms (0.3%)

series59.0ms (1.5%)

rewrite17.0ms (0.4%)

simplify90.0ms (2.4%)

prune219.0ms (5.7%)

localize11.0ms (0.3%)

series48.0ms (1.2%)

rewrite13.0ms (0.3%)

simplify69.0ms (1.8%)

prune75.0ms (1.9%)

regimes71.0ms (1.9%)

simplify3.0ms (0.1%)

end70.0ms (1.8%)

Profiling