Details

analyze1.3s (29.4%)

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 (32.2%)

Results

981.0ms	8256×	body	128	valid
302.0ms	2598×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	98	13
4	258	11
5	542	11
6	1019	11
7	1302	11
8	1414	11
9	1470	11
10	1476	11
11	1481	11
12	1481	11
13	1408	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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.6b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	8.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	5.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series38.0ms (0.9%)

Counts

2 → 88

Calls

2 calls:

29.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
9.0ms	(/.f64 (-.f64 t z) a)

rewrite8.0ms (0.2%)

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-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(/.f64 (-.f64 t z) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-rgt-in_binary64`
684×	`distribute-lft-in_binary64`
583×	`times-frac_binary64`
453×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1607
1	238	1462
2	525	1460
3	1333	1460
4	4886	1460
5	4983	1460

prune43.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Error

0.0b

Counts

80 → 4

Alt Table

Status	Error	Program
	6.1b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a)) x)
	8.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	5.6b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	1.3b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

Compiler

Compiled 1159 to 321 computations (72.3% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series22.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

22.0ms

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

simplify64.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

426×	`distribute-lft-neg-out_binary64`
425×	`distribute-rgt-neg-out_binary64`
378×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

70 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	863
1	76	750
2	164	733
3	450	733
4	2142	733
5	4579	733
6	5069	733

prune13.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	27	4	31

Error

0.0b

Counts

31 → 4

Alt Table

Status	Error	Program
▶	6.1b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a)) x)
	8.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	5.6b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	1.3b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

Compiler

Compiled 391 to 116 computations (70.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
✓	0.5b	(cbrt.f64 (-.f64 t z))
✓	5.4b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a)) x)

series114.0ms (2.6%)

Counts

4 → 144

Calls

4 calls:

34.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a)) x)
34.0ms	(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
23.0ms	(cbrt.f64 (-.f64 t z))
21.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
49×	`cbrt-prod_binary64`
38×	`cbrt-div_binary64`
36×	`associate-r_binary64`

Counts

4 → 154

Calls

4 calls:

16.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a))
8.0ms	(*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))
2.0ms	(cbrt.f64 (-.f64 t z))
0.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a)) x)

simplify143.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-def_binary64`
594×	`times-frac_binary64`
410×	`associate-l_binary64`
383×	`associate-r_binary64`
224×	`*-commutative_binary64`

Counts

298 → 291

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	5928
1	981	5615
2	3385	5374
3	5108	5374

prune254.0ms (5.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	393	0	393
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	393	4	397

Error

0.0b

Counts

397 → 4

Alt Table

Status	Error	Program
✓	6.1b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a)) x)
▶	8.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	5.6b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	1.3b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

Compiler

Compiled 12080 to 4172 computations (65.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	0.0b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	8.1b	(/.f64 (*.f64 y (-.f64 z t)) a)

series55.0ms (1.3%)

Counts

3 → 144

Calls

3 calls:

29.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
19.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
39×	`prod-diff_binary64`
37×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`

Counts

3 → 121

Calls

3 calls:

6.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
5.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
5.0ms	(*.f64 y (-.f64 z t))

simplify114.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
746×	`times-frac_binary64`
299×	`exp-prod_binary64`
213×	`cancel-sign-sub-inv_binary64`
208×	`fma-neg_binary64`

Counts

265 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	268	3653
1	555	3282
2	2075	2974
3	4562	2896
4	4877	2896

prune103.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	194	5	199

Error

Counts

199 → 5

Alt Table

Status	Error	Program
✓	5.6b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	8.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	8.2b	(-.f64 x (/.f64 (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z) (neg.f64 (.f64 t 1))) y) (.f64 (fma.f64 (neg.f64 t) 1 (*.f64 t 1)) y)) a))
	34.8b	(/.f64 y (/.f64 a (-.f64 t z)))
✓	1.3b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

Compiler

Compiled 3904 to 957 computations (75.5% saved)

regimes356.0ms (8.3%)

Accuracy

Total 1.7b remaining (99.1%)

Threshold costs 0b (0%)

Counts

36 → 3

Compiler

Compiled 6089 to 3527 computations (42.1% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	51
1	23	51
2	31	51
3	35	51
4	37	51
5	37	51

end74.0ms (1.7%)

Compiler: Compiled 167 to 88 computations (47.3% saved)

Details

analyze1.3s (29.4%)

sample1.4s (32.2%)

simplify66.0ms (1.5%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series38.0ms (0.9%)

rewrite8.0ms (0.2%)

simplify81.0ms (1.9%)

prune43.0ms (1%)

localize7.0ms (0.2%)

series22.0ms (0.5%)

rewrite1.0ms (0%)

simplify64.0ms (1.5%)

prune13.0ms (0.3%)

localize12.0ms (0.3%)

series114.0ms (2.6%)

rewrite40.0ms (0.9%)

simplify143.0ms (3.3%)

prune254.0ms (5.9%)

localize6.0ms (0.1%)

series55.0ms (1.3%)

rewrite24.0ms (0.6%)

simplify114.0ms (2.7%)

prune103.0ms (2.4%)

regimes356.0ms (8.3%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end74.0ms (1.7%)

Profiling