Details

analyze1.3s (8.6%)

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
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)

sample1.2s (7.8%)

Results

1.1s	8253×	body	128	valid
101.0ms	778×	body	128	invalid
1.0ms	2×	body	2048	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify116.0ms (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

prune3.0ms (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
	12.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
▶	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series57.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

38.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
20.0ms	(/.f64 t (-.f64 a z))

rewrite7.0ms (0%)

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:

4.0ms	(/.f64 t (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

simplify77.0ms (0.5%)

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

prune95.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	104	6	110

Error

0.0b

Counts

110 → 6

Alt Table

Status	Error	Program
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	35.6b	(fma.f64 (-.f64 y z) (*.f64 (sqrt.f64 t) (/.f64 (sqrt.f64 t) (-.f64 a z))) x)
	35.5b	(*.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)))
	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)))
▶	1.6b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	2.5b	(+.f64 (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))) x)

Compiler

Compiled 2536 to 800 computations (68.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series107.0ms (0.7%)

Counts

4 → 111

Calls

4 calls:

53.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
26.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
19.0ms	(/.f64 y (-.f64 a z))
9.0ms	(/.f64 z (-.f64 a z))

rewrite605.0ms (3.9%)

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:

55.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
32.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
4.0ms	(/.f64 z (-.f64 a z))
4.0ms	(/.f64 y (-.f64 a z))

simplify2.0s (13.1%)

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	2426	87989
2	4585	87650
3	5024	87650

prune1.3s (8.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	1694	2	1696
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	1697	5	1702

Error

Counts

1702 → 5

Alt Table

Status	Error	Program
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	35.6b	(fma.f64 (-.f64 y z) (*.f64 (sqrt.f64 t) (/.f64 (sqrt.f64 t) (-.f64 a z))) x)
	31.8b	(+.f64 (.f64 t (-.f64 (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z)))) x)
	9.1b	(+.f64 (*.f64 t (-.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3)) (/.f64 z (-.f64 a z)))) x)
▶	2.5b	(+.f64 (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))) x)

Compiler

Compiled 96348 to 16718 computations (82.6% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 t (-.f64 a z))
✓	9.8b	(*.f64 (-.f64 y z) (/.f64 t (-.f64 a z)))

series34.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

34.0ms

(*.f64 (-.f64 y z) (/.f64 t (-.f64 a z)))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
19×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`

Counts

1 → 48

Calls

1 calls:

12.0ms

(*.f64 (-.f64 y z) (/.f64 t (-.f64 a z)))

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

746×	`times-frac_binary64`
599×	`fma-def_binary64`
494×	`fma-neg_binary64`
311×	`distribute-rgt-in_binary64`
300×	`cancel-sign-sub-inv_binary64`

Counts

96 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	2608
1	524	2527
2	2022	2051
3	4819	2048
4	5163	2048

prune114.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	157	5	162

Error

Counts

162 → 5

Alt Table

Status	Error	Program
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	35.6b	(fma.f64 (-.f64 y z) (*.f64 (sqrt.f64 t) (/.f64 (sqrt.f64 t) (-.f64 a z))) x)
	31.8b	(+.f64 (.f64 t (-.f64 (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z)))) x)
▶	9.1b	(+.f64 (*.f64 t (-.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3)) (/.f64 z (-.f64 a z)))) x)
✓	2.5b	(+.f64 (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))) x)

Compiler

Compiled 3683 to 1145 computations (68.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 a z))
✓	0.2b	(pow.f64 (/.f64 y (-.f64 a z)) 3)
✓	2.7b	(*.f64 t (-.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3)) (/.f64 z (-.f64 a z))))
✓	26.9b	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3))

series163.0ms (1%)

Counts

3 → 120

Calls

3 calls:

79.0ms	(*.f64 t (-.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3)) (/.f64 z (-.f64 a z))))
51.0ms	(pow.f64 (/.f64 y (-.f64 a z)) 3)
33.0ms	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3))

rewrite1.2s (7.5%)

Algorithm

1×	rewrite-expression-head

Rules

3010×	`add-sqr-sqrt_binary64`
2973×	`*-un-lft-identity_binary64`
2891×	`times-frac_binary64`
2142×	`prod-diff_binary64`
2076×	`cbrt-prod_binary64`

Counts

3 → 2348

Calls

3 calls:

117.0ms	(*.f64 t (-.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3)) (/.f64 z (-.f64 a z))))
7.0ms	(cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3))
6.0ms	(pow.f64 (/.f64 y (-.f64 a z)) 3)

simplify3.6s (23.2%)

Algorithm

1×	egg-herbie

Rules

592×	`*-commutative_binary64`
430×	`fma-udef_binary64`
416×	`distribute-rgt-in_binary64`
300×	`unsub-neg_binary64`
291×	`times-frac_binary64`

Counts

2468 → 1448

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1904	171711
1	2985	133414
2	4746	133387
3	4831	133387
4	5032	133387

prune1.5s (9.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1505	0	1505
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1505	5	1510

Error

Counts

1510 → 5

Alt Table

Status	Error	Program
	12.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	35.6b	(fma.f64 (-.f64 y z) (*.f64 (sqrt.f64 t) (/.f64 (sqrt.f64 t) (-.f64 a z))) x)
	31.8b	(+.f64 (.f64 t (-.f64 (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z)))) x)
✓	9.1b	(+.f64 (*.f64 t (-.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a z)) 3)) (/.f64 z (-.f64 a z)))) x)
✓	2.5b	(+.f64 (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))) x)

Compiler

Compiled 93572 to 22772 computations (75.7% saved)

regimes1.8s (11.6%)

Accuracy

Total 0.6b remaining (96.7%)

Threshold costs 0.6b (96.7%)

Counts

156 → 3

Compiler

Compiled 23062 to 13424 computations (41.8% saved)

bsearch6.0ms (0%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`*-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	115
1	56	111
2	70	111
3	78	111
4	82	111
5	83	111
6	82	111

end106.0ms (0.7%)

Compiler: Compiled 264 to 122 computations (53.8% saved)

Details

analyze1.3s (8.6%)

sample1.2s (7.8%)

simplify116.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0%)

series57.0ms (0.4%)

rewrite7.0ms (0%)

simplify77.0ms (0.5%)

prune95.0ms (0.6%)

localize9.0ms (0.1%)

series107.0ms (0.7%)

rewrite605.0ms (3.9%)

simplify2.0s (13.1%)

prune1.3s (8.3%)

localize9.0ms (0.1%)

series34.0ms (0.2%)

rewrite16.0ms (0.1%)

simplify88.0ms (0.6%)

prune114.0ms (0.7%)

localize13.0ms (0.1%)

series163.0ms (1%)

rewrite1.2s (7.5%)

simplify3.6s (23.2%)

prune1.5s (9.3%)

regimes1.8s (11.6%)

bsearch6.0ms (0%)

simplify6.0ms (0%)

end106.0ms (0.7%)

Profiling