Details

analyze991.0ms (14.1%)

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
0%	99.8%	0.2%	7
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (17.7%)

Results

1.1s	8256×	body	128	valid
80.0ms	729×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1028×	`fma-neg_binary64`
470×	`fma-def_binary64`
271×	`associate-/l*_binary64`
255×	`cancel-sign-sub-inv_binary64`
255×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	53	13
3	109	13
4	185	13
5	336	13
6	549	13
7	870	13
8	1606	13
9	1757	13
10	1912	13
11	1986	13
12	1980	13
13	1985	13
14	1993	13
15	1993	13
16	1872	13

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

3.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.5b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	4.2b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	4.1b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series58.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

34.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
17.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
7.0ms	(/.f64 2 (-.f64 y t))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64`
180×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
67×	`associate-r_binary64`

Counts

3 → 234

Calls

3 calls:

17.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
6.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
3.0ms	(/.f64 2 (-.f64 y t))

simplify213.0ms (3%)

Algorithm

1×	egg-herbie

Rules

292×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
234×	`associate-/r*_binary64`
216×	`times-frac_binary64`
212×	`*-commutative_binary64`

Counts

342 → 351

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	422	7256
1	1123	6896
2	3980	6860
3	4623	6847
4	4989	6847

prune263.0ms (3.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	341	10	351
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	342	11	353

Error

0.0b

Counts

353 → 11

Alt Table

Status	Error	Program
	6.5b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.6b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
▶	3.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	5.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
	4.5b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	4.9b	(.f64 x (/.f64 2 (.f64 z (-.f64 y t))))
	35.3b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
	4.7b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	33.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	31.5b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (-.f64 y t))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) (cbrt.f64 z)))
✓	4.2b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

Compiler

Compiled 7664 to 3614 computations (52.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	2.5b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))

series208.0ms (3%)

Counts

4 → 84

Calls

4 calls:

70.0ms	(/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
68.0ms	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
34.0ms	(cbrt.f64 z)

rewrite115.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

402×	`times-frac_binary64`
272×	`add-sqr-sqrt_binary64`
264×	`*-un-lft-identity_binary64`
226×	`associate-r_binary64`
192×	`add-cube-cbrt_binary64`

Counts

4 → 344

Calls

4 calls:

37.0ms	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
5.0ms	(/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify191.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

602×	`associate-*r/_binary64`
541×	`associate-*l/_binary64`
520×	`associate-/l*_binary64`
308×	`times-frac_binary64`
304×	`associate-/r*_binary64`

Counts

428 → 460

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	471	12675
1	1431	9905
2	5253	9905

prune450.0ms (6.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	492	2	494
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	494	11	505

Error

Counts

505 → 11

Alt Table

Status	Error	Program
	6.5b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.6b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
✓	3.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	7.1b	(/.f64 (.f64 (.f64 x (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (-.f64 y t))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z)))
	33.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	5.4b	(.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 (/.f64 2 (-.f64 y t))))) (/.f64 (cbrt.f64 (/.f64 2 (-.f64 y t))) z))
▶	4.5b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	4.9b	(.f64 x (/.f64 2 (.f64 z (-.f64 y t))))
	4.7b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	32.0b	(neg.f64 (fma.f64 (/.f64 2 t) (/.f64 x z) (/.f64 (.f64 (.f64 2 x) y) (.f64 z (.f64 t t)))))
	31.5b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (-.f64 y t))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) (cbrt.f64 z)))

Compiler

Compiled 15764 to 7875 computations (50% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z)
✓	0.4b	(*.f64 x (sqrt.f64 2))
✓	0.5b	(/.f64 (sqrt.f64 2) (-.f64 y t))
✓	4.2b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))

series170.0ms (2.4%)

Counts

4 → 120

Calls

4 calls:

87.0ms	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
67.0ms	(/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z)
13.0ms	(/.f64 (sqrt.f64 2) (-.f64 y t))
3.0ms	(*.f64 x (sqrt.f64 2))

rewrite94.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

456×	`times-frac_binary64`
321×	`add-sqr-sqrt_binary64`
317×	`*-un-lft-identity_binary64`
219×	`add-cube-cbrt_binary64`
127×	`sqrt-prod_binary64`

Counts

4 → 383

Calls

4 calls:

23.0ms	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
11.0ms	(/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z)
5.0ms	(/.f64 (sqrt.f64 2) (-.f64 y t))
3.0ms	(*.f64 x (sqrt.f64 2))

simplify206.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

557×	`associate-l_binary64`
418×	`associate-r_binary64`
413×	`associate-/l*_binary64`
317×	`times-frac_binary64`
312×	`associate-*r/_binary64`

Counts

503 → 498

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	475	12011
1	1351	11333
2	5339	11333

prune420.0ms (6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	496	2	498
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	500	9	509

Error

Counts

509 → 9

Alt Table

Status	Error	Program
	6.6b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
✓	3.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	6.5b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)
	33.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	4.9b	(.f64 x (/.f64 2 (.f64 z (-.f64 y t))))
	4.7b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
▶	4.3b	(.f64 (.f64 (*.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	32.0b	(neg.f64 (fma.f64 (/.f64 2 t) (/.f64 x z) (/.f64 (.f64 (.f64 2 x) y) (.f64 z (.f64 t t)))))
	31.5b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (-.f64 y t))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) (cbrt.f64 z)))

Compiler

Compiled 12956 to 7373 computations (43.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
✓	0.3b	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
	0.5b	(/.f64 (sqrt.f64 2) (-.f64 y t))
✓	4.2b	(.f64 (.f64 (*.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))

series110.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

99.0ms

(*.f64 (*.f64 (*.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))

7.0ms

(*.f64 (*.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

5.0ms

(*.f64 x (sqrt.f64 (sqrt.f64 2)))

rewrite67.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`times-frac_binary64`
140×	`add-sqr-sqrt_binary64`
134×	`*-un-lft-identity_binary64`
130×	`associate-r_binary64`
98×	`add-cube-cbrt_binary64`

Counts

3 → 199

Calls

3 calls:

24.0ms

(*.f64 (*.f64 (*.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))

8.0ms

(*.f64 (*.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

4.0ms

(*.f64 x (sqrt.f64 (sqrt.f64 2)))

simplify204.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-r_binary64`
374×	`fma-def_binary64`
353×	`associate-/l*_binary64`
329×	`*-commutative_binary64`
324×	`associate-*r/_binary64`

Counts

271 → 271

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	338	5881
1	1045	4886
2	4185	4886
3	4727	4824
4	5000	4824
5	4970	4824

prune295.0ms (4.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	337	1	338
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	339	8	347

Error

Counts

347 → 8

Alt Table

Status	Error	Program
	6.6b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
✓	3.3b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	6.5b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)
	33.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (/.f64 2 (-.f64 y t)) (sqrt.f64 z)))
	4.7b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
✓	4.3b	(.f64 (.f64 (*.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	4.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 2) 3/2)) (/.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 y t)) z))
	31.5b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (-.f64 y t))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (sqrt.f64 (-.f64 y t))) (cbrt.f64 z)))

Compiler

Compiled 9692 to 6217 computations (35.9% saved)

regimes1.4s (19.9%)

Accuracy

Total 1.2b remaining (98.5%)

Threshold costs 0b (0%)

Counts

109 → 3

Compiler

Compiled 16184 to 11413 computations (29.5% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	78
1	40	78
2	50	78
3	56	78
4	60	78
5	61	78
6	60	78

end117.0ms (1.7%)

Compiler: Compiled 266 to 164 computations (38.3% saved)

Details

analyze991.0ms (14.1%)

sample1.2s (17.7%)

simplify97.0ms (1.4%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series58.0ms (0.8%)

rewrite53.0ms (0.8%)

simplify213.0ms (3%)

prune263.0ms (3.8%)

localize12.0ms (0.2%)

series208.0ms (3%)

rewrite115.0ms (1.6%)

simplify191.0ms (2.7%)

prune450.0ms (6.4%)

localize8.0ms (0.1%)

series170.0ms (2.4%)

rewrite94.0ms (1.3%)

simplify206.0ms (2.9%)

prune420.0ms (6%)

localize10.0ms (0.1%)

series110.0ms (1.6%)

rewrite67.0ms (1%)

simplify204.0ms (2.9%)

prune295.0ms (4.2%)

regimes1.4s (19.9%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

end117.0ms (1.7%)

Profiling