Details

analyze2.3s (20.4%)

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)

sample2.9s (26.2%)

Symmetry

(sort x y)

(sort z t)

Results

1.5s	8256×	body	128	valid
1.4s	7357×	body	128	invalid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify220.0ms (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

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

5.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.6b	(.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)

localize14.0ms (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))
✓	7.2b	(.f64 (.f64 c (fma.f64 b c a)) i)

series92.0ms (0.8%)

Counts

4 → 228

Calls

4 calls:

56.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
19.0ms	(.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))

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)
3.0ms	(*.f64 c (fma.f64 b c a))
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))

simplify133.0ms (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

prune171.0ms (1.5%)

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

0.0b

Counts

161 → 10

Alt Table

Status	Error	Program
	34.3b	(.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)))))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	6.7b	(.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)))))
	34.1b	(.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))))
	21.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	11.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	5.8b	(.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)))
	5.8b	(.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)))
	5.8b	(.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)))
▶	4.6b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))

Compiler

Compiled 4286 to 1229 computations (71.3% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
✓	0.8b	(*.f64 i (fma.f64 c b a))
✓	4.1b	(.f64 c (.f64 i (fma.f64 c b a)))

series88.0ms (0.8%)

Counts

3 → 192

Calls

3 calls:

57.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
18.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
12.0ms	(*.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)))
3.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
3.0ms	(*.f64 i (fma.f64 c b a))

simplify133.0ms (1.2%)

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	153	4703
1	336	3822
2	1163	3783
3	4522	3783
4	4977	3783
5	4931	3783

prune161.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	6	2	8
Picked	1	0	1
Done	0	1	1
Total	142	6	148

Error

Counts

148 → 6

Alt Table

Status	Error	Program
	6.7b	(.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)))))
	34.1b	(.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))))
▶	2.3b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	7.2b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	4.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) (cbrt.f64 (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 3509 to 918 computations (73.8% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))
✓	7.4b	(.f64 (.f64 c i) (fma.f64 c b a))

series81.0ms (0.7%)

Counts

2 → 144

Calls

2 calls:

62.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))
19.0ms	(.f64 (.f64 c i) (fma.f64 c b a))

rewrite12.0ms (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:

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

simplify209.0ms (1.9%)

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	128	3996
1	308	3155
2	1033	3116
3	3628	3108
4	4843	3108
5	4797	3108

prune136.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	104	6	110

Error

Counts

110 → 6

Alt Table

Status	Error	Program
	6.7b	(.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)))))
	34.1b	(.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))))
✓	2.3b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	7.2b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
▶	4.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) (cbrt.f64 (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 2749 to 730 computations (73.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) (cbrt.f64 (*.f64 i (fma.f64 c b a))))
	0.8b	(*.f64 i (fma.f64 c b a))
✓	4.1b	(.f64 c (.f64 (.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) (cbrt.f64 (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 i (fma.f64 c b a)))))
✓	7.8b	(cbrt.f64 (*.f64 i (fma.f64 c b a)))

series924.0ms (8.3%)

Counts

3 → 144

Calls

3 calls:

473.0ms

(*.f64 (cbrt.f64 (*.f64 i (fma.f64 c b a))) (cbrt.f64 (*.f64 i (fma.f64 c b a))))

388.0ms

(cbrt.f64 (*.f64 i (fma.f64 c b a)))

62.0ms

(*.f64 c (*.f64 (*.f64 (cbrt.f64 (*.f64 i (fma.f64 c b a))) (cbrt.f64 (*.f64 i (fma.f64 c b a)))) (cbrt.f64 (*.f64 i (fma.f64 c b a)))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`pow1_binary64`
14×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`pow-prod-down_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 67

Calls

3 calls:

8.0ms

(*.f64 c (*.f64 (*.f64 (cbrt.f64 (*.f64 i (fma.f64 c b a))) (cbrt.f64 (*.f64 i (fma.f64 c b a)))) (cbrt.f64 (*.f64 i (fma.f64 c b a)))))

6.0ms

(*.f64 (cbrt.f64 (*.f64 i (fma.f64 c b a))) (cbrt.f64 (*.f64 i (fma.f64 c b a))))

1.0ms

(cbrt.f64 (*.f64 i (fma.f64 c b a)))

simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

512×	`associate-r_binary64`
385×	`associate-l_binary64`
342×	`times-frac_binary64`
293×	`associate-/r*_binary64`
278×	`associate-/l*_binary64`

Counts

211 → 245

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	7430
1	1524	6762
2	5375	6762

prune533.0ms (4.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	512	0	512
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	512	6	518

Error

Counts

518 → 6

Alt Table

Status	Error	Program
	6.7b	(.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)))))
	34.1b	(.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))))
✓	2.3b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	5.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	7.2b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
✓	4.8b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 (.f64 i (fma.f64 c b a))) (cbrt.f64 (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 27815 to 10154 computations (63.5% saved)

regimes2.6s (23%)

Accuracy

Total 1.1b remaining (97.2%)

Threshold costs 0b (0%)

Counts

116 → 3

Compiler

Compiled 50227 to 32024 computations (36.2% saved)

bsearch4.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

31×	`*-commutative_binary64`
20×	`+-commutative_binary64`
18×	`sub-neg_binary64`
16×	`distribute-rgt-neg-in_binary64`
15×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	113
1	75	113
2	110	113
3	134	113
4	164	113
5	181	113
6	189	113
7	193	113
8	194	113
9	194	113

end253.0ms (2.3%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 725 to 358 computations (50.6% saved)

Iter	Nodes	Cost
0	42	113
1	75	113
2	110	113
3	134	113
4	164	113
5	181	113
6	189	113
7	193	113
8	194	113
9	194	113

Iter	Nodes	Cost
0	42	113
1	75	113
2	110	113
3	134	113
4	164	113
5	181	113
6	189	113
7	193	113
8	194	113
9	194	113

Details

analyze2.3s (20.4%)

sample2.9s (26.2%)

simplify220.0ms (2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series92.0ms (0.8%)

rewrite14.0ms (0.1%)

simplify133.0ms (1.2%)

prune171.0ms (1.5%)

localize12.0ms (0.1%)

series88.0ms (0.8%)

rewrite14.0ms (0.1%)

simplify133.0ms (1.2%)

prune161.0ms (1.4%)

localize14.0ms (0.1%)

series81.0ms (0.7%)

rewrite12.0ms (0.1%)

simplify209.0ms (1.9%)

prune136.0ms (1.2%)

localize18.0ms (0.2%)

series924.0ms (8.3%)

rewrite20.0ms (0.2%)

simplify117.0ms (1.1%)

prune533.0ms (4.8%)

regimes2.6s (23%)

bsearch4.0ms (0%)

simplify7.0ms (0.1%)

end253.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	42	113
1	75	113
2	110	113
3	134	113
4	164	113
5	181	113
6	189	113
7	193	113
8	194	113
9	194	113