Details

analyze958.0ms (16.3%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (26.2%)

Results

1.1s	8256×	body	128	valid
367.0ms	2946×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
795×	`div-sub_binary64`
536×	`times-frac_binary64`
518×	`neg-mul-1_binary64`
376×	`distribute-frac-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	27	20
2	65	20
3	126	20
4	278	20
5	602	20
6	1317	19
7	2853	19
8	4446	19
9	4743	19
10	4991	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

13.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.9b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	28.2b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	2.4b	(-.f64 (.f64 z z) (.f64 x x))
✓	14.3b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series63.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

28.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
28.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
61×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64`
49×	`prod-diff_binary64`

Counts

3 → 137

Calls

3 calls:

13.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
5.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
3.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify129.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
355×	`distribute-rgt-in_binary64`
349×	`distribute-lft-in_binary64`
265×	`fma-neg_binary64`
183×	`exp-prod_binary64`

Counts

233 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	4494
1	395	4071
2	1546	3650
3	4392	3650
4	4970	3650

prune133.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	191	5	196
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	193	5	198

Error

0.0b

Counts

198 → 5

Alt Table

Status	Error	Program
	13.9b	(.f64 -1/2 (-.f64 (/.f64 (fma.f64 z z (neg.f64 (.f64 x x))) y) y))
	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	13.9b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
	14.2b	(.f64 -1/2 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 (.f64 z z) (.f64 x x)) (cbrt.f64 y)) (neg.f64 y)))

Compiler

Compiled 5233 to 1302 computations (75.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
✓	0.0b	(/.f64 y (-.f64 z x))
✓	0.2b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

series66.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

27.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
23.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
16.0ms	(/.f64 y (-.f64 z x))

rewrite151.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

753×	`times-frac_binary64`
750×	`*-un-lft-identity_binary64`
545×	`add-sqr-sqrt_binary64`
402×	`add-cube-cbrt_binary64`
267×	`prod-diff_binary64`

Counts

3 → 543

Calls

3 calls:

32.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
8.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
5.0ms	(/.f64 y (-.f64 z x))

simplify438.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

361×	`fma-neg_binary64`
213×	`associate-*l/_binary64`
202×	`associate-/l*_binary64`
199×	`associate-/r/_binary64`
183×	`*-commutative_binary64`

Counts

639 → 561

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	17494
1	881	16388
2	3922	15169
3	4593	15169
4	4939	15169

prune343.0ms (5.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	558	3	561
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	561	5	566

Error

Counts

566 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
▶	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) y) (-.f64 z x)) y))
	13.9b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
	13.9b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 y) (/.f64 (+.f64 z x) (/.f64 1 (-.f64 z x)))) y))
	0.7b	(.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 z x))))) y))

Compiler

Compiled 18096 to 4017 computations (77.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (/.f64 (+.f64 z x) y) (-.f64 z x)) y)
✓	0.0b	(/.f64 (+.f64 z x) y)
✓	0.2b	(*.f64 (/.f64 (+.f64 z x) y) (-.f64 z x))

series58.0ms (1%)

Counts

3 → 96

Calls

3 calls:

27.0ms	(-.f64 (*.f64 (/.f64 (+.f64 z x) y) (-.f64 z x)) y)
22.0ms	(*.f64 (/.f64 (+.f64 z x) y) (-.f64 z x))
9.0ms	(/.f64 (+.f64 z x) y)

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
26×	`associate--l+_binary64`

Counts

3 → 150

Calls

3 calls:

11.0ms	(*.f64 (/.f64 (+.f64 z x) y) (-.f64 z x))
10.0ms	(-.f64 (*.f64 (/.f64 (+.f64 z x) y) (-.f64 z x)) y)
4.0ms	(/.f64 (+.f64 z x) y)

simplify141.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

677×	`distribute-rgt-in_binary64`
543×	`fma-neg_binary64`
214×	`associate-l_binary64`
195×	`times-frac_binary64`
190×	`associate-r_binary64`

Counts

246 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	3984
1	526	3750
2	2322	3623
3	4782	3623
4	4939	3623

prune185.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	246	2	248
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	248	5	253

Error

Counts

253 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) y) (-.f64 z x)) y))
	13.9b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 y) (/.f64 (+.f64 z x) (/.f64 1 (-.f64 z x)))) y))
▶	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 (/.f64 y (+.f64 z x))) (-.f64 z x)) y))
	0.5b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 z x) y)) (cbrt.f64 (/.f64 (+.f64 z x) y))) (.f64 (cbrt.f64 (/.f64 (+.f64 z x) y)) (-.f64 z x))) y))

Compiler

Compiled 6157 to 1745 computations (71.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (/.f64 1 (/.f64 y (+.f64 z x))) (-.f64 z x)) y)
✓	0.0b	(/.f64 y (+.f64 z x))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 y (+.f64 z x))) (-.f64 z x))
✓	0.7b	(/.f64 1 (/.f64 y (+.f64 z x)))

series81.0ms (1.4%)

Counts

4 → 132

Calls

4 calls:

29.0ms	(-.f64 (*.f64 (/.f64 1 (/.f64 y (+.f64 z x))) (-.f64 z x)) y)
24.0ms	(*.f64 (/.f64 1 (/.f64 y (+.f64 z x))) (-.f64 z x))
19.0ms	(/.f64 y (+.f64 z x))
9.0ms	(/.f64 1 (/.f64 y (+.f64 z x)))

rewrite76.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
192×	`*-un-lft-identity_binary64`
154×	`add-sqr-sqrt_binary64`
138×	`add-cube-cbrt_binary64`
59×	`associate-l_binary64`

Counts

4 → 300

Calls

4 calls:

18.0ms	(*.f64 (/.f64 1 (/.f64 y (+.f64 z x))) (-.f64 z x))
16.0ms	(-.f64 (*.f64 (/.f64 1 (/.f64 y (+.f64 z x))) (-.f64 z x)) y)
7.0ms	(/.f64 1 (/.f64 y (+.f64 z x)))
4.0ms	(/.f64 y (+.f64 z x))

simplify231.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-neg_binary64`
301×	`associate-l_binary64`
266×	`associate-r_binary64`
239×	`exp-prod_binary64`
224×	`cancel-sign-sub-inv_binary64`

Counts

432 → 443

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	7096
1	693	6545
2	3116	6215
3	4536	6215
4	4907	6215

prune358.0ms (6.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	443	5	448

Error

Counts

448 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) y) (-.f64 z x)) y))
	13.9b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 y) (/.f64 (+.f64 z x) (/.f64 1 (-.f64 z x)))) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 (/.f64 y (+.f64 z x))) (-.f64 z x)) y))
	0.5b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 z x) y)) (cbrt.f64 (/.f64 (+.f64 z x) y))) (.f64 (cbrt.f64 (/.f64 (+.f64 z x) y)) (-.f64 z x))) y))

Compiler

Compiled 11646 to 4418 computations (62.1% saved)

regimes666.0ms (11.3%)

Accuracy

Total 0.1b remaining (61.4%)

Threshold costs 0.1b (61.4%)

Counts

101 → 1

Compiler

Compiled 15035 to 8633 computations (42.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	17	19
2	25	19
3	29	19
4	31	19
5	31	19

end72.0ms (1.2%)

Compiler: Compiled 133 to 79 computations (40.6% saved)

Details

analyze958.0ms (16.3%)

sample1.5s (26.2%)

simplify78.0ms (1.3%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series63.0ms (1.1%)

rewrite37.0ms (0.6%)

simplify129.0ms (2.2%)

prune133.0ms (2.3%)

localize8.0ms (0.1%)

series66.0ms (1.1%)

rewrite151.0ms (2.6%)

simplify438.0ms (7.4%)

prune343.0ms (5.8%)

localize9.0ms (0.2%)

series58.0ms (1%)

rewrite38.0ms (0.6%)

simplify141.0ms (2.4%)

prune185.0ms (3.1%)

localize9.0ms (0.2%)

series81.0ms (1.4%)

rewrite76.0ms (1.3%)

simplify231.0ms (3.9%)

prune358.0ms (6.1%)

regimes666.0ms (11.3%)

simplify3.0ms (0%)

end72.0ms (1.2%)

Profiling