Details

analyze1.4s (25.8%)

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)

sample1.4s (27.1%)

Results

984.0ms	8256×	body	128	valid
330.0ms	2635×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify68.0ms (1.3%)

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

prune4.0ms (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
	8.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	5.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize7.0ms (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))
✓	7.0b	(/.f64 (*.f64 y (-.f64 z t)) a)

series59.0ms (1.1%)

Counts

3 → 144

Calls

3 calls:

30.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
22.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))

rewrite26.0ms (0.5%)

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:

7.0ms	(/.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))

simplify122.0ms (2.3%)

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

prune147.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	189	6	195
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	189	8	197

Error

Counts

197 → 8

Alt Table

Status	Error	Program
	3.1b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	8.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	37.5b	(-.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 (.f64 y (-.f64 z t)) (.f64 y (-.f64 z t))) (.f64 y (-.f64 z t))) (.f64 (*.f64 a a) a))))
	5.9b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	5.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	6.1b	(-.f64 x (/.f64 (+.f64 (.f64 z y) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) y)) a))
	7.3b	(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
▶	2.0b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

Compiler

Compiled 4099 to 1066 computations (74% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

series23.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

23.0ms

(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)

simplify69.0ms (1.3%)

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

prune26.0ms (0.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

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

Error

Counts

41 → 8

Alt Table

Status	Error	Program
▶	3.1b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	8.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	37.5b	(-.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 (.f64 y (-.f64 z t)) (.f64 y (-.f64 z t))) (.f64 y (-.f64 z t))) (.f64 (*.f64 a a) a))))
	5.9b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	5.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	6.1b	(-.f64 x (/.f64 (+.f64 (.f64 z y) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) y)) a))
	7.3b	(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	2.0b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

Compiler

Compiled 658 to 274 computations (58.4% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
✓	0.6b	(cbrt.f64 a)
✓	0.6b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	5.5b	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))

series605.0ms (11.5%)

Counts

4 → 96

Calls

4 calls:

463.0ms	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
59.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))
49.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
33.0ms	(cbrt.f64 a)

rewrite42.0ms (0.8%)

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:

17.0ms	(.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)

simplify123.0ms (2.3%)

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

prune197.0ms (3.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	269	1	270
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	270	8	278

Error

Counts

278 → 8

Alt Table

Status	Error	Program
✓	3.1b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	8.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	5.9b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	5.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	6.1b	(-.f64 x (/.f64 (+.f64 (.f64 z y) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) y)) a))
	19.7b	(-.f64 x (.f64 (.f64 y (cbrt.f64 (/.f64 1 (*.f64 a a)))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	7.3b	(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	2.0b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

Compiler

Compiled 6173 to 1640 computations (73.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
	0.0b	(*.f64 y (-.f64 z t))
✓	7.0b	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

series54.0ms (1%)

Counts

2 → 108

Calls

2 calls:

31.0ms	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
22.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`prod-exp_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 64

Calls

2 calls:

8.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))
4.0ms	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

640×	`distribute-rgt-in_binary64`
634×	`distribute-lft-in_binary64`
446×	`fma-def_binary64`
168×	`distribute-rgt-neg-in_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

172 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2142
1	384	2076
2	1335	1918
3	5314	1918

prune150.0ms (2.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	191	8	199

Error

Counts

199 → 8

Alt Table

Status	Error	Program
✓	3.1b	(-.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	8.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	5.9b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	5.9b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	6.1b	(-.f64 x (/.f64 (+.f64 (.f64 z y) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) y)) a))
	19.7b	(-.f64 x (.f64 (.f64 y (cbrt.f64 (/.f64 1 (*.f64 a a)))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	7.3b	(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	2.0b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

Compiler

Compiled 3578 to 1332 computations (62.8% saved)

regimes536.0ms (10.2%)

Accuracy

Total 1.4b remaining (99.3%)

Threshold costs 0b (0%)

Counts

37 → 3

Compiler

Compiled 5984 to 3727 computations (37.7% saved)

bsearch1.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	59
1	27	59
2	40	59
3	54	59
4	66	59
5	80	59
6	86	59
7	82	59

end101.0ms (1.9%)

Compiler: Compiled 230 to 123 computations (46.5% saved)

Details

analyze1.4s (25.8%)

sample1.4s (27.1%)

simplify68.0ms (1.3%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series59.0ms (1.1%)

rewrite26.0ms (0.5%)

simplify122.0ms (2.3%)

prune147.0ms (2.8%)

localize7.0ms (0.1%)

series23.0ms (0.4%)

rewrite1.0ms (0%)

simplify69.0ms (1.3%)

prune26.0ms (0.5%)

localize19.0ms (0.4%)

series605.0ms (11.5%)

rewrite42.0ms (0.8%)

simplify123.0ms (2.3%)

prune197.0ms (3.7%)

localize8.0ms (0.1%)

series54.0ms (1%)

rewrite15.0ms (0.3%)

simplify63.0ms (1.2%)

prune150.0ms (2.9%)

regimes536.0ms (10.2%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end101.0ms (1.9%)

Profiling