Details

analyze949.0ms (12.1%)

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
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.2s (15%)

Results

1.1s	8256×	body	128	valid
41.0ms	347×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify90.0ms (1.1%)

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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.2b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series155.0ms (2%)

Counts

4 → 153

Calls

4 calls:

68.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
44.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
39.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 t z) x)

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

4 → 115

Calls

4 calls:

13.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
7.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
6.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 t z) x)

simplify148.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
290×	`associate--l+_binary64`
218×	`fma-def_binary64`

Counts

268 → 293

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	437	10265
1	1359	9717
2	5098	9717

prune429.0ms (5.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	287	6	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	6	294

Error

0.0b

Counts

294 → 6

Alt Table

Status	Error	Program
	7.0b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	14.5b	(/.f64 (+.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	17.1b	(.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))))
	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
▶	1.1b	(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)))

Compiler

Compiled 10796 to 3968 computations (63.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.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)))
✓	3.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	7.1b	(/.f64 z (-.f64 (*.f64 t z) x))

series122.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

90.0ms	(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)))
17.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
16.0ms	(/.f64 x (-.f64 (*.f64 t z) x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

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)))

simplify171.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

400×	`times-frac_binary64`
326×	`fma-neg_binary64`
313×	`associate-/l*_binary64`
305×	`sub-neg_binary64`
241×	`associate-+r+_binary64`

Counts

192 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	6888
1	973	6477
2	4210	6352
3	4995	6350
4	5047	6350

prune333.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	263	7	270

Error

0.0b

Counts

270 → 7

Alt Table

Status	Error	Program
	7.0b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	14.5b	(/.f64 (+.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	17.1b	(.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))))
	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
▶	1.4b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (-.f64 (.f64 t z) x) (cbrt.f64 z))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
✓	1.1b	(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)))

Compiler

Compiled 10517 to 3987 computations (62.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 z)
✓	2.7b	(/.f64 (-.f64 (*.f64 t z) x) (cbrt.f64 z))
	3.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	4.7b	(/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (-.f64 (.f64 t z) x) (cbrt.f64 z)))

series305.0ms (3.9%)

Counts

3 → 84

Calls

3 calls:

251.0ms	(/.f64 (-.f64 (*.f64 t z) x) (cbrt.f64 z))
34.0ms	(cbrt.f64 z)
20.0ms	(/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (-.f64 (.f64 t z) x) (cbrt.f64 z)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
33×	`cbrt-prod_binary64`

Counts

3 → 123

Calls

3 calls:

8.0ms	(/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (-.f64 (.f64 t z) x) (cbrt.f64 z)))
7.0ms	(/.f64 (-.f64 (*.f64 t z) x) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify162.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-neg_binary64`
498×	`*-commutative_binary64`
252×	`fma-def_binary64`
227×	`unswap-sqr_binary64`
174×	`div-sub_binary64`

Counts

207 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	4976
1	554	4309
2	2181	4121
3	3853	4091
4	4881	4091
5	4970	4091

prune458.0ms (5.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	341	7	348

Error

0.0b

Counts

348 → 7

Alt Table

Status	Error	Program
	7.0b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	14.5b	(/.f64 (+.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	17.1b	(.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))))
▶	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
✓	1.4b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (-.f64 (.f64 t z) x) (cbrt.f64 z))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
✓	1.1b	(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)))

Compiler

Compiled 14541 to 4119 computations (71.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.2b	(/.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))
✓	9.4b	(/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x))

series161.0ms (2.1%)

Counts

3 → 144

Calls

3 calls:

73.0ms

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

49.0ms

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

39.0ms

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

rewrite50.0ms (0.6%)

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:

18.0ms

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

10.0ms

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

6.0ms

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

simplify172.0ms (2.2%)

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

prune504.0ms (6.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	387	0	387
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	387	7	394

Error

0.0b

Counts

394 → 7

Alt Table

Status	Error	Program
	7.0b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
	14.5b	(/.f64 (+.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))) (+.f64 x 1))
	17.1b	(.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))))
✓	6.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
✓	1.4b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (-.f64 (.f64 t z) x) (cbrt.f64 z))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
✓	1.1b	(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)))

Compiler

Compiled 14447 to 5524 computations (61.8% saved)

regimes2.2s (28.2%)

Accuracy

Total 2.0b remaining (99%)

Threshold costs 0b (0%)

Counts

321 → 1

Compiler

Compiled 47366 to 27463 computations (42% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	47
1	35	47
2	42	47
3	45	47
4	46	47
5	44	47

end122.0ms (1.6%)

Compiler: Compiled 313 to 155 computations (50.5% saved)

Details

analyze949.0ms (12.1%)

sample1.2s (15%)

simplify90.0ms (1.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series155.0ms (2%)

rewrite36.0ms (0.5%)

simplify148.0ms (1.9%)

prune429.0ms (5.5%)

localize12.0ms (0.2%)

series122.0ms (1.6%)

rewrite12.0ms (0.2%)

simplify171.0ms (2.2%)

prune333.0ms (4.3%)

localize16.0ms (0.2%)

series305.0ms (3.9%)

rewrite24.0ms (0.3%)

simplify162.0ms (2.1%)

prune458.0ms (5.8%)

localize12.0ms (0.2%)

series161.0ms (2.1%)

rewrite50.0ms (0.6%)

simplify172.0ms (2.2%)

prune504.0ms (6.4%)

regimes2.2s (28.2%)

simplify3.0ms (0%)

end122.0ms (1.6%)

Profiling