Details

analyze515.0ms (5.4%)

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
25%	74.9%	0.2%	6
25%	74.9%	0.2%	7
37.4%	62.4%	0.2%	8
37.4%	62.4%	0.2%	9
37.4%	62.4%	0.2%	10
37.4%	62.4%	0.2%	11
51.5%	48.3%	0.2%	12
56.9%	42.9%	0.2%	13
56.9%	42.9%	0.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample842.0ms (8.8%)

Infinites

7.9% of outputs are infinite.

Results

742.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify100.0ms (1%)

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

3.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.4b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	4.7b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 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)
✓	4.3b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series71.0ms (0.7%)

Counts

3 → 108

Calls

3 calls:

41.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
18.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
12.0ms	(/.f64 2 (-.f64 y t))

rewrite54.0ms (0.6%)

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:

15.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
11.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
4.0ms	(/.f64 2 (-.f64 y t))

simplify204.0ms (2.1%)

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

prune293.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	343	8	351
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	344	9	353

Error

Counts

353 → 9

Alt Table

Status	Error	Program
	30.3b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (sqrt.f64 z))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (sqrt.f64 z)))
	4.7b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	1.2b	(.f64 (.f64 x (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	32.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	4.7b	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))
	4.8b	(.f64 x (/.f64 2 (.f64 (-.f64 y t) z)))
	46.7b	(.f64 (.f64 x (/.f64 2 (-.f64 (pow.f64 y 3) (pow.f64 t 3)))) (/.f64 (+.f64 (.f64 y y) (+.f64 (.f64 t t) (*.f64 y t))) z))
	29.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
	5.5b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Compiler

Compiled 7671 to 3601 computations (53.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 (-.f64 y t))
✓	0.6b	(cbrt.f64 z)
✓	1.4b	(.f64 x (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series1.4s (14.7%)

Counts

4 → 96

Calls

4 calls:

1.3s	(.f64 x (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
38.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
32.0ms	(cbrt.f64 (-.f64 y t))
29.0ms	(cbrt.f64 z)

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
35×	`add-sqr-sqrt_binary64`
29×	`prod-exp_binary64`
25×	`associate-r_binary64`
24×	`cbrt-prod_binary64`

Counts

4 → 132

Calls

4 calls:

19.0ms	(.f64 x (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
2.0ms	(cbrt.f64 (-.f64 y t))
1.0ms	(cbrt.f64 z)

simplify141.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
489×	`associate-r_binary64`
434×	`associate-l_binary64`
324×	`associate-/r*_binary64`
239×	`times-frac_binary64`

Counts

228 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	498	6432
1	1284	5485
2	4813	5445
3	5274	5445

prune347.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	397	0	397
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	397	9	406

Error

Counts

406 → 9

Alt Table

Status	Error	Program
	30.3b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (sqrt.f64 z))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (sqrt.f64 z)))
	4.7b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
✓	1.2b	(.f64 (.f64 x (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	32.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
▶	4.7b	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))
	4.8b	(.f64 x (/.f64 2 (.f64 (-.f64 y t) z)))
	46.7b	(.f64 (.f64 x (/.f64 2 (-.f64 (pow.f64 y 3) (pow.f64 t 3)))) (/.f64 (+.f64 (.f64 y y) (+.f64 (.f64 t t) (*.f64 y t))) z))
	29.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (/.f64 2 (-.f64 y t)) z)))
	5.5b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Compiler

Compiled 17355 to 7799 computations (55.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z)
✓	0.4b	(/.f64 (-.f64 y t) (sqrt.f64 2))
✓	0.5b	(/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2)))
✓	4.3b	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))

series147.0ms (1.5%)

Counts

4 → 132

Calls

4 calls:

70.0ms	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))
44.0ms	(/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z)
23.0ms	(/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2)))
10.0ms	(/.f64 (-.f64 y t) (sqrt.f64 2))

rewrite594.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Rules

4403×	`times-frac_binary64`
2465×	`add-sqr-sqrt_binary64`
2432×	`*-un-lft-identity_binary64`
1830×	`add-cube-cbrt_binary64`
1577×	`sqrt-prod_binary64`

Counts

4 → 1839

Calls

4 calls:

110.0ms	(*.f64 x (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z))
35.0ms	(/.f64 (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2))) z)
10.0ms	(/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (sqrt.f64 2)))
10.0ms	(/.f64 (-.f64 y t) (sqrt.f64 2))

simplify1.2s (12.4%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/r*_binary64`
728×	`times-frac_binary64`
462×	`associate-/l/_binary64`
428×	`associate-/r/_binary64`
280×	`*-commutative_binary64`

Counts

1971 → 1728

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1229	61250
1	3132	59975
2	5356	59975

prune1.8s (18.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1725	3	1728
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	1730	7	1737

Error

Counts

1737 → 7

Alt Table

Status	Error	Program
▶	3.9b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
	4.4b	(.f64 x (.f64 (sqrt.f64 2) (/.f64 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 y t)) (sqrt.f64 (sqrt.f64 2))) z)))
	4.8b	(.f64 x (/.f64 2 (.f64 (-.f64 y t) z)))
	30.3b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (sqrt.f64 z))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (sqrt.f64 z)))
✓	1.2b	(.f64 (.f64 x (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	5.7b	(.f64 (.f64 x (/.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 y t))) (/.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) z))
	5.5b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Compiler

Compiled 53293 to 33228 computations (37.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y t) z)
✓	3.9b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))

series46.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

38.0ms	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
7.0ms	(*.f64 (-.f64 y t) z)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`

Counts

2 → 49

Calls

2 calls:

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

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

675×	`associate-*l/_binary64`
416×	`fma-def_binary64`
269×	`associate-/l/_binary64`
252×	`times-frac_binary64`
249×	`associate-/r/_binary64`

Counts

121 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2122
1	430	1885
2	2015	1807
3	5418	1807

prune76.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Error

Counts

92 → 6

Alt Table

Status	Error	Program
	5.7b	(.f64 (.f64 x (/.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 y t))) (/.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) z))
	6.9b	(/.f64 2 (/.f64 (-.f64 y t) (/.f64 x z)))
✓	3.9b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
	4.4b	(.f64 x (.f64 (sqrt.f64 2) (/.f64 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 2)) (-.f64 y t)) (sqrt.f64 (sqrt.f64 2))) z)))
✓	1.2b	(.f64 (.f64 x (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	5.5b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)

Compiler

Compiled 1584 to 694 computations (56.2% saved)

regimes1.5s (15.4%)

Accuracy

Total 1.6b remaining (99.1%)

Threshold costs 0b (0%)

Counts

204 → 1

Compiler

Compiled 29629 to 21066 computations (28.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	24	46
2	28	46
3	30	46
4	31	46
5	30	46

end98.0ms (1%)

Compiler: Compiled 184 to 116 computations (37% saved)

Details

analyze515.0ms (5.4%)

sample842.0ms (8.8%)

simplify100.0ms (1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series71.0ms (0.7%)

rewrite54.0ms (0.6%)

simplify204.0ms (2.1%)

prune293.0ms (3.1%)

localize18.0ms (0.2%)

series1.4s (14.7%)

rewrite39.0ms (0.4%)

simplify141.0ms (1.5%)

prune347.0ms (3.6%)

localize8.0ms (0.1%)

series147.0ms (1.5%)

rewrite594.0ms (6.2%)

simplify1.2s (12.4%)

prune1.8s (18.8%)

localize6.0ms (0.1%)

series46.0ms (0.5%)

rewrite14.0ms (0.2%)

simplify61.0ms (0.6%)

prune76.0ms (0.8%)

regimes1.5s (15.4%)

simplify3.0ms (0%)

end98.0ms (1%)

Profiling