Details

analyze1.2s (21.5%)

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)

sample1.5s (26.3%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify57.0ms (1%)

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

2.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.7b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	2.7b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (0.1%)

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)))))
✓	5.4b	(/.f64 (.f64 y t) (.f64 2 z))
✓	6.3b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

series98.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

57.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
25.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
16.0ms	(/.f64 (.f64 y t) (.f64 2 z))

rewrite52.0ms (0.9%)

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:

22.0ms	(-.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))

simplify194.0ms (3.4%)

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 → 254

Iterations

Useful iterations: 2 (0.0ms)

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

prune267.0ms (4.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	250	4	254
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	252	4	256

Error

Counts

256 → 4

Alt Table

Status	Error	Program
	3.0b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))) (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))) (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))))
	24.3b	(fma.f64 2 (/.f64 z t) x)
▶	0.8b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))

Compiler

Compiled 10001 to 5097 computations (49% saved)

localize10.0ms (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)))))
✓	6.0b	(*.f64 (/.f64 y 2) (/.f64 t z))
✓	6.3b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

series135.0ms (2.4%)

Counts

3 → 120

Calls

3 calls:

77.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
40.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
17.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))

rewrite40.0ms (0.7%)

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:

13.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
7.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
3.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

simplify203.0ms (3.6%)

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

prune243.0ms (4.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	245	4	249

Error

Counts

249 → 4

Alt Table

Status	Error	Program
	2.8b	(-.f64 x (/.f64 y (-.f64 z (.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z))))))
	24.3b	(fma.f64 2 (/.f64 z t) x)
✓	0.8b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
▶	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))

Compiler

Compiled 8892 to 4564 computations (48.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
✓	0.5b	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
	5.4b	(/.f64 (.f64 y t) (.f64 2 z))
✓	5.9b	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))

series96.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

41.0ms	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
30.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
24.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 109

Calls

3 calls:

22.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
6.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
3.0ms	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))

simplify170.0ms (3%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
234×	`fma-neg_binary64`
231×	`associate-/r/_binary64`
206×	`associate-/l/_binary64`
205×	`distribute-rgt-neg-in_binary64`

Counts

229 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	6000
1	624	5773
2	2130	5441
3	4879	5441
4	4927	5441

prune227.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	250	4	254

Error

Counts

254 → 4

Alt Table

Status	Error	Program
▶	2.8b	(-.f64 x (/.f64 y (-.f64 z (.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z))))))
	24.3b	(fma.f64 2 (/.f64 z t) x)
✓	0.8b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))

Compiler

Compiled 6447 to 3549 computations (45% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	3.8b	(.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z)))
✓	6.3b	(/.f64 y (-.f64 z (.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z)))))

series157.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

48.0ms	(.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z)))
40.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
37.0ms	(cbrt.f64 z)
32.0ms	(/.f64 y (-.f64 z (.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z)))))

rewrite88.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-exp-log_binary64`
71×	`prod-exp_binary64`
56×	`add-cbrt-cube_binary64`
46×	`div-exp_binary64`
42×	`add-sqr-sqrt_binary64`

Counts

4 → 174

Calls

4 calls:

14.0ms	(.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z)))
7.0ms	(/.f64 y (-.f64 z (.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z)))))
6.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify188.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

339×	`associate-l_binary64`
316×	`fma-def_binary64`
281×	`associate-r_binary64`
249×	`associate-*l/_binary64`
238×	`unswap-sqr_binary64`

Counts

270 → 268

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	322	5679
1	754	4153
2	3346	4088
3	4423	4081
4	4977	4081
5	4976	4081

prune269.0ms (4.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	304	0	304
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	304	4	308

Error

Counts

308 → 4

Alt Table

Status	Error	Program
✓	2.8b	(-.f64 x (/.f64 y (-.f64 z (.f64 (.f64 (/.f64 y 2) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 t (cbrt.f64 z))))))
	24.3b	(fma.f64 2 (/.f64 z t) x)
✓	0.8b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))

Compiler

Compiled 8878 to 3954 computations (55.5% saved)

regimes332.0ms (5.8%)

Accuracy

Total 1.1b remaining (99.5%)

Threshold costs 0b (0%)

Counts

31 → 1

Compiler

Compiled 4078 to 2638 computations (35.3% 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

end73.0ms (1.3%)

Compiler: Compiled 106 to 69 computations (34.9% saved)

Details

analyze1.2s (21.5%)

sample1.5s (26.3%)

simplify57.0ms (1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series98.0ms (1.7%)

rewrite52.0ms (0.9%)

simplify194.0ms (3.4%)

prune267.0ms (4.7%)

localize10.0ms (0.2%)

series135.0ms (2.4%)

rewrite40.0ms (0.7%)

simplify203.0ms (3.6%)

prune243.0ms (4.3%)

localize10.0ms (0.2%)

series96.0ms (1.7%)

rewrite38.0ms (0.7%)

simplify170.0ms (3%)

prune227.0ms (4%)

localize15.0ms (0.3%)

series157.0ms (2.8%)

rewrite88.0ms (1.5%)

simplify188.0ms (3.3%)

prune269.0ms (4.7%)

regimes332.0ms (5.8%)

simplify3.0ms (0.1%)

end73.0ms (1.3%)

Profiling