Details

analyze1.1s (25.6%)

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 (26.8%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify55.0ms (1.3%)

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

2.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.4b	(-.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 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	5.1b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
✓	5.8b	(/.f64 (.f64 y t) (.f64 2 z))

series85.0ms (2%)

Counts

3 → 120

Calls

3 calls:

43.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
28.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
14.0ms	(/.f64 (.f64 y t) (.f64 2 z))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64`
105×	`*-un-lft-identity_binary64`
77×	`times-frac_binary64`
71×	`add-cube-cbrt_binary64`
63×	`prod-diff_binary64`

Counts

3 → 165

Calls

3 calls:

12.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify186.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

325×	`cancel-sign-sub-inv_binary64`
304×	`distribute-neg-frac_binary64`
221×	`times-frac_binary64`
203×	`associate-/l*_binary64`
182×	`associate-*r/_binary64`

Counts

285 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	384	10579
1	1057	7887
2	3351	6717
3	4786	6717

prune227.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	250	4	254

Error

0.0b

Counts

254 → 4

Alt Table

Status	Error	Program
	24.2b	(-.f64 x (/.f64 y z))
	7.2b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3)))
▶	0.3b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	22.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 9907 to 5047 computations (49.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	5.1b	(*.f64 (/.f64 y 2) (/.f64 t z))
✓	5.1b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

series94.0ms (2.2%)

Counts

3 → 120

Calls

3 calls:

44.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
31.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
18.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
68×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

3 → 162

Calls

3 calls:

11.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
8.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
3.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

simplify199.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-def_binary64`
241×	`associate-*r/_binary64`
221×	`associate-*l/_binary64`
198×	`fma-neg_binary64`
193×	`*-commutative_binary64`

Counts

282 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	9065
1	1098	7039
2	3324	6174
3	4775	6174
4	4814	6174

prune210.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	245	4	249

Error

0.0b

Counts

249 → 4

Alt Table

Status	Error	Program
	24.2b	(-.f64 x (/.f64 y z))
▶	7.2b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3)))
✓	0.3b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	22.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 8860 to 4546 computations (48.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3)
✓	5.1b	(/.f64 y (*.f64 2 (/.f64 z t)))
✓	5.1b	(/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))
✓	27.4b	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3))

series151.0ms (3.5%)

Counts

4 → 144

Calls

4 calls:

64.0ms	(pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3)
40.0ms	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3))
32.0ms	(/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))
14.0ms	(/.f64 y (*.f64 2 (/.f64 z t)))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`*-un-lft-identity_binary64`
86×	`add-sqr-sqrt_binary64`
78×	`times-frac_binary64`
54×	`add-cube-cbrt_binary64`
48×	`cbrt-prod_binary64`

Counts

4 → 189

Calls

4 calls:

8.0ms	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3))
7.0ms	(pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3)
6.0ms	(/.f64 y (*.f64 2 (/.f64 z t)))
5.0ms	(/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t)))))

simplify213.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
489×	`unswap-sqr_binary64`
212×	`associate-/l*_binary64`
207×	`times-frac_binary64`
176×	`sqr-pow_binary64`

Counts

333 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	9653
1	933	9167
2	3498	8964
3	5317	8964

prune210.0ms (4.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	209	4	213

Error

0.0b

Counts

213 → 4

Alt Table

Status	Error	Program
	24.2b	(-.f64 x (/.f64 y z))
✓	7.2b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3)))
✓	0.3b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
▶	22.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 5944 to 3466 computations (41.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z t) x)

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(fma.f64 2 (/.f64 z t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 2 (/.f64 z t) x)

simplify75.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-*l/_binary64`
542×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
443×	`associate-+l+_binary64`
396×	`fma-def_binary64`

Counts

46 → 14

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	376
1	23	359
2	49	359
3	126	359
4	432	359
5	1628	359
6	4283	359
7	4686	359
8	4929	359
9	4999	359

prune11.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	14	4	18

Error

0.0b

Counts

18 → 4

Alt Table

Status	Error	Program
	24.2b	(-.f64 x (/.f64 y z))
✓	7.2b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (-.f64 z (/.f64 y (*.f64 2 (/.f64 z t))))) 3)))
✓	0.3b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	22.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 195 to 106 computations (45.6% saved)

regimes109.0ms (2.5%)

Accuracy

Total 1.0b remaining (99.3%)

Threshold costs 0b (0%)

Counts

15 → 1

Compiler

Compiled 1654 to 1102 computations (33.4% 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

end63.0ms (1.4%)

Compiler: Compiled 90 to 60 computations (33.3% saved)

Details

analyze1.1s (25.6%)

sample1.2s (26.8%)

simplify55.0ms (1.3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series85.0ms (2%)

rewrite43.0ms (1%)

simplify186.0ms (4.3%)

prune227.0ms (5.2%)

localize9.0ms (0.2%)

series94.0ms (2.2%)

rewrite42.0ms (1%)

simplify199.0ms (4.6%)

prune210.0ms (4.8%)

localize13.0ms (0.3%)

series151.0ms (3.5%)

rewrite45.0ms (1%)

simplify213.0ms (4.9%)

prune210.0ms (4.8%)

localize6.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify75.0ms (1.7%)

prune11.0ms (0.2%)

regimes109.0ms (2.5%)

simplify3.0ms (0.1%)

end63.0ms (1.4%)

Profiling