Details

analyze1.3s (19.8%)

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)

sample1.5s (22.8%)

Results

1.1s	8256×	body	128	valid
329.0ms	2608×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify71.0ms (1.1%)

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%)

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
	5.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	5.3b	(-.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 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))
✓	6.1b	(/.f64 (*.f64 y (-.f64 z t)) a)

series61.0ms (0.9%)

Counts

3 → 144

Calls

3 calls:

30.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
24.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms	(*.f64 y (-.f64 z t))

rewrite28.0ms (0.4%)

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

simplify126.0ms (1.9%)

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

prune162.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	188	7	195
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	189	8	197

Error

0.0b

Counts

197 → 8

Alt Table

Status	Error	Program
	34.9b	(-.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
▶	2.9b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	3.5b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	36.9b	(/.f64 y (/.f64 a (-.f64 t z)))
	5.3b	(-.f64 x (/.f64 (*.f64 y (-.f64 t z)) (neg.f64 a)))
	23.6b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y (-.f64 z t)) a) (/.f64 (.f64 y (-.f64 z t)) a)) (/.f64 (*.f64 y (-.f64 z t)) a))))
	5.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	33.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)) (sqrt.f64 (fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)))

Compiler

Compiled 4119 to 1073 computations (73.9% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.8b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

series25.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

25.0ms

(fma.f64 (/.f64 y a) (fma.f64 -1 z t) 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) (fma.f64 -1 z t) x)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-neg-out_binary64`
399×	`distribute-lft-neg-out_binary64`
377×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
227×	`distribute-rgt-out_binary64`

Counts

70 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	875
1	79	750
2	165	733
3	440	733
4	2134	733
5	4825	733
6	5128	733

prune29.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	33	8	41

Error

0.0b

Counts

41 → 8

Alt Table

Status	Error	Program
	34.9b	(-.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
✓	2.9b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
▶	3.5b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	36.9b	(/.f64 y (/.f64 a (-.f64 t z)))
	33.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
	5.3b	(-.f64 x (/.f64 (*.f64 y (-.f64 t z)) (neg.f64 a)))
	23.6b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y (-.f64 z t)) a) (/.f64 (.f64 y (-.f64 z t)) a)) (/.f64 (*.f64 y (-.f64 z t)) a))))
	5.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 674 to 271 computations (59.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	5.6b	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))

series612.0ms (9.2%)

Counts

4 → 96

Calls

4 calls:

479.0ms	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
50.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
48.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))
36.0ms	(cbrt.f64 a)

rewrite38.0ms (0.6%)

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:

14.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))
7.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
4.0ms	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
1.0ms	(cbrt.f64 a)

simplify131.0ms (2%)

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

prune184.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	269	1	270
Fresh	0	6	6
Picked	0	1	1
Done	1	0	1
Total	270	8	278

Error

Counts

278 → 8

Alt Table

Status	Error	Program
✓	3.5b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	36.9b	(/.f64 y (/.f64 a (-.f64 t z)))
	5.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	3.6b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a))))))
	33.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
	34.9b	(-.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
	5.3b	(-.f64 x (/.f64 (*.f64 y (-.f64 t z)) (neg.f64 a)))
	23.6b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y (-.f64 z t)) a) (/.f64 (.f64 y (-.f64 z t)) a)) (/.f64 (*.f64 y (-.f64 z t)) a))))

Compiler

Compiled 6251 to 1656 computations (73.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 a)
✓	0.6b	(cbrt.f64 (cbrt.f64 a))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
✓	5.6b	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a)))))

series619.0ms (9.3%)

Counts

3 → 72

Calls

3 calls:

317.0ms

(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))

254.0ms

(cbrt.f64 (cbrt.f64 a))

48.0ms

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

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`

Counts

3 → 77

Calls

3 calls:

19.0ms

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

2.0ms

(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))

1.0ms

(cbrt.f64 (cbrt.f64 a))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-/l/_binary64`
444×	`*-commutative_binary64`
398×	`fma-def_binary64`
191×	`associate-/r/_binary64`
189×	`log-div_binary64`

Counts

149 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3546
1	389	2803
2	1809	2448
3	4387	2448
4	4974	2448

prune143.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	204	8	212

Error

Counts

212 → 8

Alt Table

Status	Error	Program
✓	3.5b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	36.9b	(/.f64 y (/.f64 a (-.f64 t z)))
	5.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	3.6b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a))))))
	33.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
	34.9b	(-.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
	5.3b	(-.f64 x (/.f64 (*.f64 y (-.f64 t z)) (neg.f64 a)))
	23.6b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y (-.f64 z t)) a) (/.f64 (.f64 y (-.f64 z t)) a)) (/.f64 (*.f64 y (-.f64 z t)) a))))

Compiler

Compiled 6227 to 1277 computations (79.5% saved)

regimes1.2s (18.3%)

Accuracy

Total 0.6b remaining (96.4%)

Threshold costs 0.6b (96.4%)

Counts

78 → 3

Compiler

Compiled 14452 to 8608 computations (40.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

46×	`distribute-rgt-neg-in_binary64`
34×	`cancel-sign-sub-inv_binary64`
31×	`distribute-lft-neg-in_binary64`
25×	`neg-sub0_binary64`
25×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	65
1	42	63
2	59	63
3	75	63
4	107	63
5	125	63
6	144	63
7	167	63
8	199	63
9	228	63
10	239	63
11	246	63
12	248	63
13	244	63

end104.0ms (1.6%)

Compiler: Compiled 261 to 136 computations (47.9% saved)

Iter	Nodes	Cost
0	28	65
1	42	63
2	59	63
3	75	63
4	107	63
5	125	63
6	144	63
7	167	63
8	199	63
9	228	63
10	239	63
11	246	63
12	248	63
13	244	63

Iter	Nodes	Cost
0	28	65
1	42	63
2	59	63
3	75	63
4	107	63
5	125	63
6	144	63
7	167	63
8	199	63
9	228	63
10	239	63
11	246	63
12	248	63
13	244	63

Details

analyze1.3s (19.8%)

sample1.5s (22.8%)

simplify71.0ms (1.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series61.0ms (0.9%)

rewrite28.0ms (0.4%)

simplify126.0ms (1.9%)

prune162.0ms (2.4%)

localize7.0ms (0.1%)

series25.0ms (0.4%)

rewrite1.0ms (0%)

simplify71.0ms (1.1%)

prune29.0ms (0.4%)

localize10.0ms (0.2%)

series612.0ms (9.2%)

rewrite38.0ms (0.6%)

simplify131.0ms (2%)

prune184.0ms (2.8%)

localize13.0ms (0.2%)

series619.0ms (9.3%)

rewrite31.0ms (0.5%)

simplify109.0ms (1.6%)

prune143.0ms (2.1%)

regimes1.2s (18.3%)

bsearch2.0ms (0%)

simplify11.0ms (0.2%)

end104.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	28	65
1	42	63
2	59	63
3	75	63
4	107	63
5	125	63
6	144	63
7	167	63
8	199	63
9	228	63
10	239	63
11	246	63
12	248	63
13	244	63