Details

analyze1.2s (26.6%)

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
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (29.8%)

Results

947.0ms	8256×	body	128	valid
301.0ms	2536×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	7.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.7b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series30.0ms (0.7%)

Counts

1 → 60

Calls

1 calls:

30.0ms

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

simplify67.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

473×	`distribute-rgt-neg-out_binary64`
446×	`distribute-lft-neg-out_binary64`
352×	`distribute-lft-in_binary64`
352×	`distribute-rgt-in_binary64`
248×	`unsub-neg_binary64`

Counts

70 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	1118
1	73	735
2	159	733
3	439	733
4	2127	733
5	4571	733
6	5081	733

prune21.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Error

0.0b

Counts

33 → 4

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
✓	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	7.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	35.3b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) (sqrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)))

Compiler

Compiled 470 to 132 computations (71.9% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 (-.f64 z t) (/.f64 y a) x)

series21.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

21.0ms

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

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-lft-neg-out_binary64`
429×	`distribute-rgt-neg-out_binary64`
368×	`distribute-rgt-in_binary64`
367×	`distribute-lft-in_binary64`
244×	`distribute-rgt-out_binary64`

Counts

70 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	1133
1	77	750
2	164	733
3	445	733
4	2171	733
5	4663	733
6	4961	733

prune11.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	26	4	30

Error

0.0b

Counts

30 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
✓	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	7.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	35.3b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)) (sqrt.f64 (fma.f64 (-.f64 z t) (/.f64 y a) x)))

Compiler

Compiled 378 to 112 computations (70.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	7.4b	(/.f64 (*.f64 y (-.f64 z t)) a)

series51.0ms (1.1%)

Counts

3 → 144

Calls

3 calls:

27.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
18.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

7.0ms	(*.f64 y (-.f64 z t))
6.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
3.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
517×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
448×	`fma-def_binary64`
124×	`associate-l_binary64`

Counts

236 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2898
1	425	2525
2	1558	2355
3	5186	2355

prune83.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	146	6	152

Error

Counts

152 → 6

Alt Table

Status	Error	Program
	7.6b	(+.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	5.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
▶	2.3b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
✓	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
✓	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	7.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 2587 to 738 computations (71.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	4.1b	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))

series703.0ms (15.5%)

Counts

4 → 96

Calls

4 calls:

579.0ms	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
49.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))
39.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
35.0ms	(cbrt.f64 a)

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
40×	`associate-r_binary64`
36×	`cbrt-prod_binary64`

Counts

4 → 151

Calls

4 calls:

15.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))
4.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
4.0ms	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
1.0ms	(cbrt.f64 a)

simplify124.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-def_binary64`
334×	`associate-/r/_binary64`
183×	`associate-*r/_binary64`
182×	`associate-/r*_binary64`
179×	`distribute-rgt-in_binary64`

Counts

247 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	4014
1	505	2982
2	2258	2923
3	3938	2868
4	5042	2868

prune154.0ms (3.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	270	6	276

Error

Counts

276 → 6

Alt Table

Status	Error	Program
	7.6b	(+.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	5.7b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	2.3b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
✓	1.3b	(fma.f64 (-.f64 z t) (/.f64 y a) x)
✓	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	7.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 6042 to 1554 computations (74.3% saved)

regimes314.0ms (6.9%)

Accuracy

Total 1.5b remaining (99.1%)

Threshold costs 0b (0%)

Counts

29 → 3

Compiler

Compiled 4202 to 2594 computations (38.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	56
1	28	56
2	32	56
3	34	56
4	35	56
5	34	56

end89.0ms (2%)

Compiler: Compiled 184 to 96 computations (47.8% saved)

Details

analyze1.2s (26.6%)

sample1.4s (29.8%)

simplify70.0ms (1.5%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series30.0ms (0.7%)

rewrite1.0ms (0%)

simplify67.0ms (1.5%)

prune21.0ms (0.5%)

localize6.0ms (0.1%)

series21.0ms (0.5%)

rewrite1.0ms (0%)

simplify71.0ms (1.6%)

prune11.0ms (0.2%)

localize10.0ms (0.2%)

series51.0ms (1.1%)

rewrite21.0ms (0.5%)

simplify71.0ms (1.6%)

prune83.0ms (1.8%)

localize10.0ms (0.2%)

series703.0ms (15.5%)

rewrite42.0ms (0.9%)

simplify124.0ms (2.7%)

prune154.0ms (3.4%)

regimes314.0ms (6.9%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end89.0ms (2%)

Profiling