Details

analyze2.6s (14%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
16.5%	83.2%	0.2%	13
25.9%	73.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.2s (11.7%)

Results

1.9s	8253×	body	128	valid
182.0ms	757×	body	128	invalid
1.0ms	1×	body	1024	valid
1.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify125.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1893×	`fma-neg_binary64`
867×	`div-sub_binary64`
749×	`fma-def_binary64`
696×	`distribute-rgt-in_binary64`
535×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	81	14
4	160	14
5	302	14
6	620	14
7	1528	14
8	2624	14
9	2858	14
10	3205	14
11	3392	14
12	3498	14
13	3533	14
14	5398	14

prune6.0ms (0%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	12.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series92.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

63.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
28.0ms	(/.f64 t (-.f64 a z))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

7.0ms	(/.f64 t (-.f64 a z))
1.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

simplify122.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary64`
633×	`fma-def_binary64`
620×	`associate-/l*_binary64`
272×	`cancel-sign-sub-inv_binary64`
175×	`associate-/l/_binary64`

Counts

133 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3215
1	492	3156
2	1711	2520
3	5110	2520

prune144.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	106	4	110

Error

0.0b

Counts

110 → 4

Alt Table

Status	Error	Program
▶	2.4b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	33.7b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 2401 to 743 computations (69.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (-.f64 a z))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	3.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series164.0ms (0.9%)

Counts

4 → 111

Calls

4 calls:

84.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
39.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
27.0ms	(/.f64 y (-.f64 a z))
14.0ms	(/.f64 z (-.f64 a z))

rewrite1.2s (6.3%)

Algorithm

1×	rewrite-expression-head

Rules

2048×	`*-un-lft-identity_binary64`
2030×	`add-sqr-sqrt_binary64`
2016×	`times-frac_binary64`
1323×	`prod-diff_binary64`
1200×	`add-cube-cbrt_binary64`

Counts

4 → 1556

Calls

4 calls:

111.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
68.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
8.0ms	(/.f64 y (-.f64 a z))
7.0ms	(/.f64 z (-.f64 a z))

simplify4.1s (21.7%)

Algorithm

1×	egg-herbie

Rules

422×	`*-commutative_binary64`
357×	`distribute-rgt-in_binary64`
306×	`fma-udef_binary64`
263×	`unsub-neg_binary64`
251×	`distribute-lft-in_binary64`

Counts

1667 → 1696

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1400	120634
1	2423	87989
2	4585	87650
3	5024	87650

prune1.6s (8.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1694	2	1696
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	1695	5	1700

Error

Counts

1700 → 5

Alt Table

Status	Error	Program
✓	2.4b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	2.6b	(+.f64 (.f64 t (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z)))) (cbrt.f64 (/.f64 y (-.f64 a z))) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z)))) x)
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	35.6b	(+.f64 (.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) x)

Compiler

Compiled 96367 to 16715 computations (82.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z))))
✓	3.3b	(.f64 t (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z)))) (cbrt.f64 (/.f64 y (-.f64 a z))) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z))))
✓	14.0b	(cbrt.f64 (/.f64 y (-.f64 a z)))
✓	51.2b	(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (*.f64 (/.f64 1 (-.f64 a z)) z))

series2.4s (13.1%)

Counts

4 → 144

Calls

4 calls:

1.5s	(.f64 t (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z)))) (cbrt.f64 (/.f64 y (-.f64 a z))) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z))))
419.0ms	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z))))
287.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (*.f64 (/.f64 1 (-.f64 a z)) z))
273.0ms	(cbrt.f64 (/.f64 y (-.f64 a z)))

rewrite54.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`cbrt-prod_binary64`
115×	`add-sqr-sqrt_binary64`
109×	`*-un-lft-identity_binary64`
93×	`times-frac_binary64`
59×	`add-cube-cbrt_binary64`

Counts

4 → 177

Calls

4 calls:

21.0ms	(*.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z))))
5.0ms	(.f64 t (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z)))) (cbrt.f64 (/.f64 y (-.f64 a z))) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z))))
4.0ms	(cbrt.f64 (/.f64 y (-.f64 a z)))
0.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (*.f64 (/.f64 1 (-.f64 a z)) z))

simplify188.0ms (1%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-l_binary64`
364×	`fma-def_binary64`
361×	`times-frac_binary64`
283×	`associate-/l*_binary64`
234×	`*-commutative_binary64`

Counts

321 → 370

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	736	12303
1	1908	11152
2	5180	11152

prune649.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	542	0	542
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	542	5	547

Error

Counts

547 → 5

Alt Table

Status	Error	Program
✓	2.4b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	2.6b	(+.f64 (.f64 t (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z)))) (cbrt.f64 (/.f64 y (-.f64 a z))) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z)))) x)
▶	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	35.6b	(+.f64 (.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) x)

Compiler

Compiled 35940 to 15569 computations (56.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	0.0b	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
✓	6.1b	(/.f64 (*.f64 y t) (-.f64 a z))
✓	12.3b	(/.f64 (*.f64 t z) (-.f64 a z))

series117.0ms (0.6%)

Counts

4 → 144

Calls

4 calls:

44.0ms	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
31.0ms	(/.f64 (*.f64 y t) (-.f64 a z))
23.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
18.0ms	(/.f64 (*.f64 t z) (-.f64 a z))

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
44×	`prod-diff_binary64`
40×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`

Counts

4 → 162

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
8.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
5.0ms	(/.f64 (*.f64 y t) (-.f64 a z))
5.0ms	(/.f64 (*.f64 t z) (-.f64 a z))

simplify196.0ms (1%)

Algorithm

1×	egg-herbie

Rules

373×	`fma-neg_binary64`
296×	`sub-neg_binary64`
224×	`associate-/l*_binary64`
191×	`times-frac_binary64`
174×	`associate-l_binary64`

Counts

306 → 288

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	382	8802
1	1080	7597
2	3913	7022
3	4564	7021
4	4834	7021

prune223.0ms (1.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	288	5	293

Error

Counts

293 → 5

Alt Table

Status	Error	Program
✓	2.4b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	2.6b	(+.f64 (.f64 t (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a z))) (cbrt.f64 (/.f64 y (-.f64 a z)))) (cbrt.f64 (/.f64 y (-.f64 a z))) (neg.f64 (.f64 (/.f64 1 (-.f64 a z)) z))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 a z))) z (.f64 (/.f64 1 (-.f64 a z)) z)))) x)
✓	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	35.6b	(+.f64 (.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) x)

Compiler

Compiled 9519 to 1785 computations (81.2% saved)

regimes2.3s (12.4%)

Accuracy

Total 0.2b remaining (94.9%)

Threshold costs 0.2b (94.9%)

Counts

214 → 3

Compiler

Compiled 50094 to 25811 computations (48.5% saved)

bsearch11.0ms (0.1%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`*-commutative_binary64`
9×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	102
1	50	102
2	64	102
3	77	102
4	84	102
5	87	102
6	88	102
7	87	102

end84.0ms (0.4%)

Compiler: Compiled 282 to 131 computations (53.5% saved)

Details

analyze2.6s (14%)

sample2.2s (11.7%)

simplify125.0ms (0.7%)

prune6.0ms (0%)

localize14.0ms (0.1%)

series92.0ms (0.5%)

rewrite14.0ms (0.1%)

simplify122.0ms (0.7%)

prune144.0ms (0.8%)

localize18.0ms (0.1%)

series164.0ms (0.9%)

rewrite1.2s (6.3%)

simplify4.1s (21.7%)

prune1.6s (8.6%)

localize18.0ms (0.1%)

series2.4s (13.1%)

rewrite54.0ms (0.3%)

simplify188.0ms (1%)

prune649.0ms (3.5%)

localize10.0ms (0.1%)

series117.0ms (0.6%)

rewrite50.0ms (0.3%)

simplify196.0ms (1%)

prune223.0ms (1.2%)

regimes2.3s (12.4%)

bsearch11.0ms (0.1%)

simplify5.0ms (0%)

end84.0ms (0.4%)

Profiling