Details

analyze18.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
99.6%	0%	0.4%	1

Compiler

Compiled 28 to 19 computations (32.1% saved)

sample2.2s (10.1%)

Symmetry

(sort x y)

(sort z t)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify273.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1133×	`distribute-rgt-in_binary64`
1066×	`distribute-lft-in_binary64`
969×	`unsub-neg_binary64`
583×	`fma-def_binary64`
461×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	37	24
2	97	24
3	277	24
4	797	24
5	1809	24
6	2532	24
7	2783	24
8	3128	24
9	3409	24
10	3319	24
11	3327	24
12	3331	24
13	3461	24
14	3620	24
15	3621	24
16	3623	24
17	3623	24
18	5071	24

prune7.0ms (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

5.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 94 to 57 computations (39.4% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 c (fma.f64 b c a))
✓	0.3b	(fma.f64 x y (*.f64 z t))
✓	1.6b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
✓	6.6b	(.f64 (.f64 c (fma.f64 b c a)) i)

series182.0ms (0.8%)

Counts

4 → 228

Calls

4 calls:

101.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
43.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
20.0ms	(*.f64 c (fma.f64 b c a))
17.0ms	(fma.f64 x y (*.f64 z t))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 73

Calls

4 calls:

4.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
4.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
3.0ms	(*.f64 c (fma.f64 b c a))
0.0ms	(fma.f64 x y (*.f64 z t))

simplify158.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
563×	`distribute-rgt-in_binary64`
556×	`distribute-lft-in_binary64`
505×	`fma-def_binary64`
242×	`cancel-sign-sub-inv_binary64`

Counts

301 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	4992
1	327	4027
2	1091	3988
3	4531	3988
4	4933	3988

prune341.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	152	9	161

Error

0.2b

Counts

161 → 9

Alt Table

Status	Error	Program
	27.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 c (fma.f64 b c a))) (.f64 c (fma.f64 b c a))) (.f64 (.f64 i i) i)))))
	18.6b	(.f64 2 (-.f64 (.f64 t z) (.f64 c (.f64 i (fma.f64 c b a)))))
	18.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 c 2) (.f64 i b))))
	34.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (fma.f64 b c a))) i)))
	15.6b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i a))))
	34.8b	(.f64 2 (.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
▶	6.0b	(.f64 2 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
✓	5.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	17.4b	(.f64 2 (-.f64 (.f64 y x) (.f64 c (.f64 i (fma.f64 c b a)))))

Compiler

Compiled 4164 to 1171 computations (71.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))))
	1.6b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
	6.6b	(.f64 (.f64 c (fma.f64 b c a)) i)
✓	26.4b	(cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i)))

series10.7s (48.4%)

Counts

2 → 192

Calls

2 calls:

8.1s

(*.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))))

2.7s

(cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`cbrt-div_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

9.0ms

(*.f64 (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i))))

7.0ms

(cbrt.f64 (-.f64 (fma.f64 x y (*.f64 z t)) (*.f64 (*.f64 c (fma.f64 b c a)) i)))

simplify824.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

257 → 241

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7620	106758

prune2.9s (13.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	745	0	745
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	745	9	754

Error

0.2b

Counts

754 → 9

Alt Table

Status	Error	Program
	27.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 c (fma.f64 b c a))) (.f64 c (fma.f64 b c a))) (.f64 (.f64 i i) i)))))
	18.6b	(.f64 2 (-.f64 (.f64 t z) (.f64 c (.f64 i (fma.f64 c b a)))))
	18.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 c 2) (.f64 i b))))
	34.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (fma.f64 b c a))) i)))
▶	15.6b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i a))))
	34.8b	(.f64 2 (.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
✓	6.0b	(.f64 2 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
✓	5.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	17.4b	(.f64 2 (-.f64 (.f64 y x) (.f64 c (.f64 i (fma.f64 c b a)))))

Compiler

Compiled 143794 to 76360 computations (46.9% saved)

localize22.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i a)))
✓	3.9b	(.f64 c (.f64 i a))

series111.0ms (0.5%)

Counts

2 → 100

Calls

2 calls:

93.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i a)))
19.0ms	(.f64 c (.f64 i a))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 41

Calls

2 calls:

9.0ms	(.f64 c (.f64 i a))
4.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i a)))

simplify126.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-+l+_binary64`
537×	`associate-+r+_binary64`
346×	`distribute-rgt-neg-in_binary64`
337×	`distribute-lft-neg-in_binary64`
332×	`fma-def_binary64`

Counts

141 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	2043
1	204	1984
2	692	1956
3	2123	1949
4	4969	1949

prune146.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	78	8	86

Error

0.2b

Counts

86 → 8

Alt Table

Status	Error	Program
▶	13.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) a)))
	18.6b	(.f64 2 (-.f64 (.f64 t z) (.f64 c (.f64 i (fma.f64 c b a)))))
	18.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 c 2) (.f64 i b))))
	34.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (fma.f64 b c a))) i)))
	34.8b	(.f64 2 (.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
✓	6.0b	(.f64 2 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
✓	5.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	17.4b	(.f64 2 (-.f64 (.f64 y x) (.f64 c (.f64 i (fma.f64 c b a)))))

Compiler

Compiled 1976 to 619 computations (68.7% saved)

localize32.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) a))
✓	3.8b	(.f64 (.f64 c i) a)

series91.0ms (0.4%)

Counts

2 → 120

Calls

2 calls:

69.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) a))
21.0ms	(.f64 (.f64 c i) a)

rewrite32.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 41

Calls

2 calls:

23.0ms	(.f64 (.f64 c i) a)
5.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) a))

simplify120.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

558×	`associate-+l+_binary64`
547×	`associate-+r+_binary64`
380×	`fma-def_binary64`
376×	`distribute-rgt-neg-in_binary64`
351×	`distribute-lft-neg-in_binary64`

Counts

161 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	2185
1	216	2126
2	775	2098
3	2254	2091
4	5199	2091

prune138.0ms (0.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	76	8	84

Error

0.2b

Counts

84 → 8

Alt Table

Status	Error	Program
✓	13.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) a)))
	18.6b	(.f64 2 (-.f64 (.f64 t z) (.f64 c (.f64 i (fma.f64 c b a)))))
	18.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (pow.f64 c 2) (.f64 i b))))
	34.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (fma.f64 b c a))) i)))
	34.8b	(.f64 2 (.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
✓	6.0b	(.f64 2 (.f64 (.f64 (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))) (cbrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
✓	5.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	17.4b	(.f64 2 (-.f64 (.f64 y x) (.f64 c (.f64 i (fma.f64 c b a)))))

Compiler

Compiled 1789 to 514 computations (71.3% saved)

regimes3.2s (14.6%)

Accuracy

Total 3.3b remaining (92.4%)

Threshold costs 0b (0%)

Counts

73 → 3

Compiler

Compiled 42260 to 22042 computations (47.8% saved)

bsearch7.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
12×	`+-commutative_binary64`
11×	`sub-neg_binary64`
8×	`distribute-rgt-neg-in_binary64`
8×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	98
1	60	98
2	83	98
3	102	98
4	114	98
5	119	98
6	120	98
7	120	98

end287.0ms (1.3%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 703 to 349 computations (50.4% saved)

Details

analyze18.0ms (0.1%)

sample2.2s (10.1%)

simplify273.0ms (1.2%)

prune7.0ms (0%)

localize27.0ms (0.1%)

series182.0ms (0.8%)

rewrite15.0ms (0.1%)

simplify158.0ms (0.7%)

prune341.0ms (1.5%)

localize17.0ms (0.1%)

series10.7s (48.4%)

rewrite28.0ms (0.1%)

simplify824.0ms (3.7%)

prune2.9s (13.3%)

localize22.0ms (0.1%)

series111.0ms (0.5%)

rewrite17.0ms (0.1%)

simplify126.0ms (0.6%)

prune146.0ms (0.7%)

localize32.0ms (0.1%)

series91.0ms (0.4%)

rewrite32.0ms (0.1%)

simplify120.0ms (0.5%)

prune138.0ms (0.6%)

regimes3.2s (14.6%)

bsearch7.0ms (0%)

simplify14.0ms (0.1%)

end287.0ms (1.3%)

Profiling