Details

analyze2.2s (22.4%)

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 28 to 19 computations (32.1% saved)

sample121.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort x y)

(sort z t)

Results

22.0ms	256×	body	128	valid
13.0ms	196×	body	128	invalid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify226.0ms (2.3%)

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

prune4.0ms (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

9.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.9b	(.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)

localize12.0ms (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 (*.f64 c (fma.f64 b c a)) i))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	11.4b	(.f64 (.f64 c (fma.f64 b c a)) i)

series103.0ms (1.1%)

Counts

4 → 228

Calls

4 calls:

55.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
26.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
13.0ms	(*.f64 c (fma.f64 b c a))
9.0ms	(fma.f64 x y (*.f64 z t))

rewrite14.0ms (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))

simplify121.0ms (1.2%)

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

prune147.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	153	8	161

Error

0.3b

Counts

161 → 8

Alt Table

Status	Error	Program
	10.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c (.f64 (cbrt.f64 (fma.f64 b c a)) (cbrt.f64 (fma.f64 b c a)))) (cbrt.f64 (fma.f64 b c a))) i)))
	53.5b	(.f64 2 (neg.f64 (.f64 c (*.f64 i a))))
	32.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
▶	7.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	10.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	17.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	18.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i a))))
✓	9.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 4054 to 1135 computations (72% 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))))
✓	1.8b	(*.f64 i (fma.f64 c b a))
✓	6.0b	(.f64 c (.f64 i (fma.f64 c b a)))

series95.0ms (1%)

Counts

3 → 192

Calls

3 calls:

60.0ms	(-.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)))
14.0ms	(*.f64 i (fma.f64 c b a))

rewrite14.0ms (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)))
4.0ms	(*.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))))

simplify140.0ms (1.4%)

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

prune184.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	155	9	164

Error

0.0b

Counts

164 → 9

Alt Table

Status	Error	Program
	8.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	10.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	32.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
✓	7.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	8.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a))))))
	17.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	24.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (cbrt.f64 (pow.f64 (.f64 i (fma.f64 c b a)) 3)))))
▶	2.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	9.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 4006 to 1101 computations (72.5% saved)

localize12.0ms (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)))
✓	6.4b	(.f64 (.f64 c i) (fma.f64 c b a))

series78.0ms (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)))
19.0ms	(.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)))

simplify136.0ms (1.4%)

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

prune124.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	6	6
Picked	0	1	1
Done	1	1	2
Total	122	9	131

Error

0.0b

Counts

131 → 9

Alt Table

Status	Error	Program
	8.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	10.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	8.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a))))))
	17.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	24.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (cbrt.f64 (pow.f64 (.f64 i (fma.f64 c b a)) 3)))))
✓	2.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
	32.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
▶	3.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c i) (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a)))))
✓	9.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 3301 to 934 computations (71.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))
✓	1.4b	(.f64 (.f64 (.f64 c i) (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a)))
✓	2.2b	(cbrt.f64 (fma.f64 c b a))
✓	3.7b	(.f64 (.f64 c i) (*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a))))

series659.0ms (6.8%)

Counts

4 → 168

Calls

4 calls:

516.0ms	(.f64 (.f64 c i) (*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a))))
79.0ms	(*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))
43.0ms	(cbrt.f64 (fma.f64 c b a))
20.0ms	(.f64 (.f64 (.f64 c i) (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a)))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
36×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`pow-prod-down_binary64`
22×	`cbrt-prod_binary64`

Counts

4 → 111

Calls

4 calls:

26.0ms	(.f64 (.f64 c i) (*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a))))
9.0ms	(.f64 (.f64 (.f64 c i) (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a)))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))
1.0ms	(cbrt.f64 (fma.f64 c b a))

simplify248.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-def_binary64`
449×	`times-frac_binary64`
392×	`associate-/l*_binary64`
375×	`associate-/r*_binary64`
222×	`*-commutative_binary64`

Counts

279 → 289

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	552	9373
1	1730	8716
2	4814	8716
3	5022	8716

prune748.0ms (7.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	421	2	423
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	423	9	432

Error

Counts

432 → 9

Alt Table

Status	Error	Program
	3.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c i) (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 c b a))) (cbrt.f64 (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (cbrt.f64 (fma.f64 c b a)))))))
	8.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	10.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i))) (cbrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)))))
	17.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (fma.f64 c (.f64 i a) (.f64 (.f64 c c) (.f64 i b)))))
✓	2.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
	32.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (sqrt.f64 (.f64 c (fma.f64 b c a))) (sqrt.f64 (.f64 c (fma.f64 b c a)))) i)))
	8.0b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a))))))
✓	3.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c i) (.f64 (cbrt.f64 (fma.f64 c b a)) (cbrt.f64 (fma.f64 c b a)))) (cbrt.f64 (fma.f64 c b a)))))
✓	9.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 22361 to 9431 computations (57.8% saved)

regimes2.0s (20.2%)

Accuracy

Total 0.7b remaining (96.5%)

Threshold costs 0.7b (96.5%)

Counts

93 → 3

Compiler

Compiled 41135 to 25618 computations (37.7% saved)

bsearch4.0ms (0%)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
18×	`+-commutative_binary64`
15×	`sub-neg_binary64`
14×	`distribute-rgt-neg-in_binary64`
13×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	89
1	61	89
2	84	89
3	106	89
4	142	89
5	161	89
6	169	89
7	171	89
8	171	89

end19.0ms (0.2%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 340 to 170 computations (50% saved)

sample2.3s (23.4%)

Algorithm

1×

intervals

Results

655.0ms	8000×	body	128	valid
573.0ms	7378×	body	128	invalid

Compiler

Compiled 414 to 226 computations (45.4% saved)

Details

analyze2.2s (22.4%)

sample121.0ms (1.2%)

simplify226.0ms (2.3%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series103.0ms (1.1%)

rewrite14.0ms (0.1%)

simplify121.0ms (1.2%)

prune147.0ms (1.5%)

localize13.0ms (0.1%)

series95.0ms (1%)

rewrite14.0ms (0.1%)

simplify140.0ms (1.4%)

prune184.0ms (1.9%)

localize12.0ms (0.1%)

series78.0ms (0.8%)

rewrite9.0ms (0.1%)

simplify136.0ms (1.4%)

prune124.0ms (1.3%)

localize17.0ms (0.2%)

series659.0ms (6.8%)

rewrite49.0ms (0.5%)

simplify248.0ms (2.6%)

prune748.0ms (7.7%)

regimes2.0s (20.2%)

bsearch4.0ms (0%)

simplify10.0ms (0.1%)

end19.0ms (0.2%)

sample2.3s (23.4%)

Profiling