Details

analyze2.2s (18.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample2.5s (20.9%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

(sort c i)

Results

1.4s	8256×	body	128	valid
1.0s	6038×	body	128	invalid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

58×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
17×	`+-commutative_binary64`
4×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	28	16
2	61	16
3	105	16
4	121	16
5	123	16
6	123	16

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 75 to 42 computations (44% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

series49.0ms (0.4%)

Counts

2 → 144

Calls

2 calls:

40.0ms	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
9.0ms	(fma.f64 x y (*.f64 z t))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 x y (*.f64 z t))
0.0ms	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

684×	`associate-+r+_binary64`
680×	`associate-+l+_binary64`
533×	`distribute-rgt-out_binary64`
436×	`unswap-sqr_binary64`
392×	`associate-l_binary64`

Counts

164 → 53

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	1992
1	80	1942
2	158	1942
3	549	1942
4	1403	1942
5	3764	1942
6	4951	1942
7	5049	1942

prune33.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	2	54

Error

0.0b

Counts

54 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
▶	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))

Compiler

Compiled 893 to 188 computations (78.9% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a b (fma.f64 t z (*.f64 c i)))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))

series50.0ms (0.4%)

Counts

2 → 168

Calls

2 calls:

31.0ms	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
19.0ms	(fma.f64 a b (fma.f64 t z (*.f64 c i)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
0.0ms	(fma.f64 a b (fma.f64 t z (*.f64 c i)))

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

742×	`associate-+r+_binary64`
693×	`associate-+l+_binary64`
597×	`fma-def_binary64`
389×	`associate-l_binary64`
318×	`associate-r_binary64`

Counts

188 → 46

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	2448
1	77	2390
2	203	2390
3	964	2390
4	5083	2390

prune33.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	45	3	48

Error

0.0b

Counts

48 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
▶	1.0b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i))))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))))

Compiler

Compiled 792 to 151 computations (80.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y x (.f64 (.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i))))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i))))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))
✓	0.6b	(cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))

series1.2s (9.8%)

Counts

4 → 312

Calls

4 calls:

765.0ms	(.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))
341.0ms	(cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))
35.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i))))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))))
22.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i))))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i))))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))
4.0ms	(.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))
1.0ms	(cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))
0.0ms	(fma.f64 y x (.f64 (.f64 (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i)))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (.f64 c i))))) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))))

simplify353.0ms (3%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary64`
285×	`associate-*r/_binary64`
283×	`associate-/r*_binary64`
283×	`associate-/l*_binary64`
283×	`times-frac_binary64`

Counts

415 → 392

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2351	32693
1	5533	32693

prune1.2s (10.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	659	1	660
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	660	3	663

Error

0.0b

Counts

663 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
▶	34.0b	(fma.f64 y x (.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 c i)) 2)) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))))

Compiler

Compiled 81119 to 38940 computations (52% saved)

localize73.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (fma.f64 t z (*.f64 c i)) 2)
✓	0.3b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 c i)) 2)) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))
	0.6b	(cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))
✓	24.3b	(cbrt.f64 (pow.f64 (fma.f64 t z (*.f64 c i)) 2))

series1.8s (15.4%)

Counts

3 → 168

Calls

3 calls:

1.6s	(.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 c i)) 2)) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))
178.0ms	(cbrt.f64 (pow.f64 (fma.f64 t z (*.f64 c i)) 2))
24.0ms	(pow.f64 (fma.f64 t z (*.f64 c i)) 2)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`associate-l_binary64`

Counts

3 → 79

Calls

3 calls:

6.0ms	(.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 c i)) 2)) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i)))))
1.0ms	(pow.f64 (fma.f64 t z (*.f64 c i)) 2)
1.0ms	(cbrt.f64 (pow.f64 (fma.f64 t z (*.f64 c i)) 2))

simplify330.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-r_binary64`
326×	`fma-def_binary64`
199×	`associate-/r*_binary64`
180×	`associate-/l*_binary64`
174×	`times-frac_binary64`

Counts

247 → 314

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1944	32334
1	5257	32334

prune958.0ms (8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	448	0	448
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	448	3	451

Error

0.0b

Counts

451 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
✓	34.0b	(fma.f64 y x (.f64 (cbrt.f64 (pow.f64 (fma.f64 t z (.f64 c i)) 2)) (cbrt.f64 (fma.f64 a b (fma.f64 t z (*.f64 c i))))))

Compiler

Compiled 59344 to 31864 computations (46.3% saved)

regimes718.0ms (6%)

Accuracy

Total 0.0b remaining (67.7%)

Threshold costs 0.0b (67.7%)

Counts

42 → 1

Compiler

Compiled 15588 to 9420 computations (39.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	14	16
2	14	16

end151.0ms (1.3%)

Remove

(sort c i)

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 271 to 161 computations (40.6% saved)

Details

analyze2.2s (18.4%)

sample2.5s (20.9%)

simplify8.0ms (0.1%)

prune5.0ms (0%)

localize10.0ms (0.1%)

series49.0ms (0.4%)

rewrite1.0ms (0%)

simplify105.0ms (0.9%)

prune33.0ms (0.3%)

localize10.0ms (0.1%)

series50.0ms (0.4%)

rewrite1.0ms (0%)

simplify64.0ms (0.5%)

prune33.0ms (0.3%)

localize14.0ms (0.1%)

series1.2s (9.8%)

rewrite27.0ms (0.2%)

simplify353.0ms (3%)

prune1.2s (10.3%)

localize73.0ms (0.6%)

series1.8s (15.4%)

rewrite14.0ms (0.1%)

simplify330.0ms (2.8%)

prune958.0ms (8%)

regimes718.0ms (6%)

simplify2.0ms (0%)

end151.0ms (1.3%)

Profiling