Details

analyze546.0ms (8.8%)

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
25%	74.9%	0.2%	5
37.4%	62.4%	0.2%	6
37.4%	62.4%	0.2%	7
37.4%	62.4%	0.2%	8
40.5%	59.3%	0.2%	9
49.1%	50.7%	0.2%	10
49.1%	50.7%	0.2%	11
54.2%	45.6%	0.2%	12
61.4%	38.4%	0.2%	13
70.5%	29.3%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample939.0ms (15.1%)

Infinites

3.9% of outputs are infinite.

Results

848.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

6.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.7b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	10.0b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series162.0ms (2.6%)

Counts

4 → 114

Calls

4 calls:

79.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
46.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
32.0ms	(-.f64 (*.f64 t z) x)
5.0ms	(-.f64 (*.f64 y z) x)

rewrite52.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
10×	`distribute-lft-out_binary64`

Counts

4 → 117

Calls

4 calls:

23.0ms	(-.f64 (*.f64 y z) x)
12.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
7.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 t z) x)

simplify167.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
544×	`fma-neg_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
201×	`associate--l+_binary64`

Counts

231 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	8297
1	1260	7857
2	4933	7855
3	5379	7855

prune316.0ms (5.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	260	3	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	261	3	264

Error

0.0b

Counts

264 → 3

Alt Table

Status	Error	Program
▶	1.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	18.4b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))

Compiler

Compiled 9255 to 3438 computations (62.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	3.1b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.3b	(/.f64 z (-.f64 (*.f64 t z) x))

series165.0ms (2.7%)

Counts

4 → 156

Calls

4 calls:

106.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
21.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
21.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
17.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))

rewrite220.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
64×	`add-cube-cbrt_binary64`
55×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

4 → 151

Calls

4 calls:

199.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))
4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
0.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

simplify248.0ms (4%)

Algorithm

1×	egg-herbie

Rules

406×	`times-frac_binary64`
395×	`fma-neg_binary64`
363×	`associate-/l*_binary64`
249×	`associate-/r*_binary64`
140×	`associate-r_binary64`

Counts

307 → 332

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	493	12597
1	1439	9669
2	4731	9654
3	5085	9654

prune308.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	331	4	335

Error

Counts

335 → 4

Alt Table

Status	Error	Program
✓	1.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	18.4b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
▶	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	11.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

Compiler

Compiled 15089 to 4972 computations (67% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.3b	(/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))
✓	0.5b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	10.2b	(/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x))

series181.0ms (2.9%)

Counts

3 → 144

Calls

3 calls:

85.0ms

(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))) (+.f64 x 1))

51.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))

45.0ms

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

rewrite59.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

3 → 167

Calls

3 calls:

21.0ms

(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))) (+.f64 x 1))

8.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) (-.f64 (*.f64 y z) x)))

7.0ms

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

simplify213.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

513×	`times-frac_binary64`
389×	`associate-/l*_binary64`
324×	`associate-/r*_binary64`
266×	`associate--l+_binary64`
179×	`sub-neg_binary64`

Counts

311 → 360

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	480	13006
1	1499	12060
2	5108	12060

prune382.0ms (6.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	394	0	394
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	394	4	398

Error

Counts

398 → 4

Alt Table

Status	Error	Program
✓	1.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	18.4b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
✓	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
▶	11.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

Compiler

Compiled 14541 to 5563 computations (61.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (*.f64 t z) x)))
	3.1b	(/.f64 x (-.f64 (*.f64 t z) x))
	8.3b	(/.f64 z (-.f64 (*.f64 t z) x))
✓	31.8b	(cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (*.f64 t z) x))))

series61.0ms (1%)

Counts

2 → 72

Calls

2 calls:

30.0ms	(cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (*.f64 t z) x))))
30.0ms	(.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (*.f64 t z) x)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 94

Calls

2 calls:

15.0ms	(cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (*.f64 t z) x))))
13.0ms	(.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (*.f64 t z) x)))

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

586×	`associate-/l/_binary64`
499×	`fma-def_binary64`
222×	`distribute-rgt-in_binary64`
200×	`associate-/l*_binary64`
185×	`distribute-lft-in_binary64`

Counts

166 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	5391
1	705	4757
2	2562	4298
3	5204	4298

prune474.0ms (7.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	474	4	478

Error

Counts

478 → 4

Alt Table

Status	Error	Program
✓	1.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	18.4b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
✓	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	11.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (cbrt.f64 (.f64 (.f64 (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 z (-.f64 (.f64 t z) x))) (/.f64 z (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

Compiler

Compiled 24888 to 6333 computations (74.6% saved)

regimes1.2s (19.2%)

Accuracy

Total 0.6b remaining (95%)

Threshold costs 0.6b (95%)

Counts

200 → 2

Compiler

Compiled 24775 to 15489 computations (37.5% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	102
1	47	102
2	60	102
3	66	102
4	69	102
5	68	102

end226.0ms (3.6%)

Compiler: Compiled 259 to 139 computations (46.3% saved)

Details

analyze546.0ms (8.8%)

sample939.0ms (15.1%)

simplify93.0ms (1.5%)

prune2.0ms (0%)

localize11.0ms (0.2%)

series162.0ms (2.6%)

rewrite52.0ms (0.8%)

simplify167.0ms (2.7%)

prune316.0ms (5.1%)

localize12.0ms (0.2%)

series165.0ms (2.7%)

rewrite220.0ms (3.5%)

simplify248.0ms (4%)

prune308.0ms (4.9%)

localize12.0ms (0.2%)

series181.0ms (2.9%)

rewrite59.0ms (0.9%)

simplify213.0ms (3.4%)

prune382.0ms (6.1%)

localize15.0ms (0.2%)

series61.0ms (1%)

rewrite42.0ms (0.7%)

simplify109.0ms (1.7%)

prune474.0ms (7.6%)

regimes1.2s (19.2%)

bsearch8.0ms (0.1%)

simplify5.0ms (0.1%)

end226.0ms (3.6%)

Profiling