Details

analyze2.3s (24.7%)

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 28 to 19 computations (32.1% saved)

sample3.2s (33.7%)

Symmetry

(sort x y)

(sort z t)

Results

1.6s	8256×	body	128	valid
1.5s	7311×	body	128	invalid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify221.0ms (2.4%)

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

prune3.0ms (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

6.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.6b	(.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)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	8.0b	(.f64 (.f64 c (fma.f64 b c a)) i)

series102.0ms (1.1%)

Counts

4 → 228

Calls

4 calls:

61.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
22.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
9.0ms	(*.f64 c (fma.f64 b c a))
8.0ms	(fma.f64 x y (*.f64 z t))

rewrite16.0ms (0.2%)

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:

5.0ms	(*.f64 c (fma.f64 b c a))
4.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
3.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
0.0ms	(fma.f64 x y (*.f64 z t))

simplify119.0ms (1.3%)

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

prune161.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	151	9	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	10	161

Error

0.3b

Counts

161 → 10

Alt Table

Status	Error	Program
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (fma.f64 b c a))) i)))
	31.2b	(.f64 2 (.f64 (sqrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a))))) (sqrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	20.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))
	13.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i a))))
	35.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (*.f64 c (fma.f64 b c a)) (sqrt.f64 i)) (sqrt.f64 i))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)))
▶	4.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	7.6b	(.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)))))
	9.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))

Compiler

Compiled 4254 to 1221 computations (71.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a))))
✓	1.0b	(*.f64 i (fma.f64 c b a))
✓	4.0b	(.f64 c (.f64 i (fma.f64 c b a)))

series93.0ms (1%)

Counts

3 → 192

Calls

3 calls:

59.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a))))
20.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
13.0ms	(*.f64 i (fma.f64 c b a))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`fma-udef_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`

Counts

3 → 71

Calls

3 calls:

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

simplify149.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
606×	`distribute-lft-in_binary64`
552×	`fma-def_binary64`
306×	`fma-neg_binary64`
215×	`cancel-sign-sub-inv_binary64`

Counts

263 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	4703
1	332	3822
2	1163	3783
3	4522	3783
4	4977	3783
5	4931	3783

prune165.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	157	9	166

Error

0.0b

Counts

166 → 9

Alt Table

Status	Error	Program
✓	4.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
▶	2.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	20.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))
	5.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	20.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (cbrt.f64 (pow.f64 (.f64 i (fma.f64 c b a)) 3)))))
	7.6b	(.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)))))
	9.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))

Compiler

Compiled 4042 to 1103 computations (72.7% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c i) (fma.f64 c b a)))
✓	5.7b	(.f64 (.f64 c i) (fma.f64 c b a))

series76.0ms (0.8%)

Counts

2 → 144

Calls

2 calls:

58.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c i) (fma.f64 c b a)))
18.0ms	(.f64 (.f64 c i) (fma.f64 c b a))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`fma-udef_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 45

Calls

2 calls:

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

simplify118.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
516×	`fma-def_binary64`
445×	`distribute-rgt-in_binary64`
436×	`distribute-lft-in_binary64`
295×	`*-commutative_binary64`

Counts

189 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	3996
1	307	3155
2	1033	3116
3	3628	3108
4	4843	3108
5	4797	3108

prune126.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	122	9	131

Error

0.0b

Counts

131 → 9

Alt Table

Status	Error	Program
✓	4.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
✓	2.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	20.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))
▶	5.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	20.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (cbrt.f64 (pow.f64 (.f64 i (fma.f64 c b a)) 3)))))
	7.6b	(.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)))))
	9.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))

Compiler

Compiled 3286 to 914 computations (72.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (*.f64 a i))))
✓	0.2b	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))
✓	3.3b	(.f64 c (.f64 i b))
✓	4.0b	(.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))

series117.0ms (1.2%)

Counts

4 → 180

Calls

4 calls:

74.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (*.f64 a i))))
22.0ms	(.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))
13.0ms	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))
8.0ms	(.f64 c (.f64 i b))

rewrite23.0ms (0.2%)

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 → 81

Calls

4 calls:

7.0ms	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))
6.0ms	(.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))
3.0ms	(.f64 c (.f64 i b))
2.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (*.f64 a i))))

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

606×	`distribute-rgt-in_binary64`
586×	`distribute-lft-in_binary64`
334×	`fma-neg_binary64`
259×	`cancel-sign-sub-inv_binary64`
220×	`associate-l_binary64`

Counts

261 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	4603
1	433	3868
2	1530	3816
3	4607	3816
4	4934	3816

prune169.0ms (1.8%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	161	10	171

Error

Counts

171 → 10

Alt Table

Status	Error	Program
✓	4.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
✓	2.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	6.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	20.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))
✓	5.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	6.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 c (fma.f64 b c a))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) (cbrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	20.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (cbrt.f64 (pow.f64 (.f64 i (fma.f64 c b a)) 3)))))
	32.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))) (sqrt.f64 (.f64 c (+.f64 (.f64 c (.f64 i b)) (*.f64 a i)))))))
	7.6b	(.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)))))
	9.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))

Compiler

Compiled 4499 to 1099 computations (75.6% saved)

regimes1.8s (18.9%)

Accuracy

Total 1.6b remaining (98.4%)

Threshold costs 0b (0%)

Counts

76 → 3

Compiler

Compiled 35724 to 21026 computations (41.1% saved)

bsearch79.0ms (0.8%)

Steps

Iters	Range		Point
8	1.6829167338680049e-102	5.664454926740205e-98	5.5784381509619995e-98
3	-8.595573896034063e-40	-1.083040052821259e-44	-2.0943062549980613e-40

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
22×	`+-commutative_binary64`
19×	`sub-neg_binary64`
18×	`distribute-rgt-neg-in_binary64`
16×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	93
1	71	93
2	106	93
3	134	93
4	174	93
5	194	93
6	202	93
7	204	93
8	204	93

end194.0ms (2.1%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 765 to 416 computations (45.6% saved)

Details

analyze2.3s (24.7%)

sample3.2s (33.7%)

simplify221.0ms (2.4%)

prune3.0ms (0%)

localize15.0ms (0.2%)

series102.0ms (1.1%)

rewrite16.0ms (0.2%)

simplify119.0ms (1.3%)

prune161.0ms (1.7%)

localize13.0ms (0.1%)

series93.0ms (1%)

rewrite13.0ms (0.1%)

simplify149.0ms (1.6%)

prune165.0ms (1.8%)

localize14.0ms (0.1%)

series76.0ms (0.8%)

rewrite9.0ms (0.1%)

simplify118.0ms (1.3%)

prune126.0ms (1.3%)

localize15.0ms (0.2%)

series117.0ms (1.2%)

rewrite23.0ms (0.2%)

simplify117.0ms (1.2%)

prune169.0ms (1.8%)

regimes1.8s (18.9%)

bsearch79.0ms (0.8%)

simplify6.0ms (0.1%)

end194.0ms (2.1%)

Profiling