Details

analyze2.7s (27.5%)

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)

sample98.0ms (1%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
16.0ms	238×	body	128	invalid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify225.0ms (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

7.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.6b	(.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))
✓	8.2b	(.f64 (.f64 c (fma.f64 b c a)) i)

series100.0ms (1%)

Counts

4 → 228

Calls

4 calls:

60.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
20.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
10.0ms	(fma.f64 x y (*.f64 z t))
10.0ms	(*.f64 c (fma.f64 b c a))

rewrite12.0ms (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))

simplify123.0ms (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

prune183.0ms (1.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	148	12	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	148	13	161

Error

0.3b

Counts

161 → 13

Alt Table

Status	Error	Program
▶	5.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (fma.f64 c b a)))))
	34.2b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (*.f64 c (sqrt.f64 (fma.f64 b c a))) (sqrt.f64 (fma.f64 b c a))) i)))
	5.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a))))) (cbrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))))))
	21.6b	(.f64 2 (fma.f64 t z (.f64 y x)))
	10.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	20.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))
✓	7.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	7.9b	(.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)))
	32.7b	(.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)))
	7.9b	(.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)))
	17.5b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (expm1.f64 (log1p.f64 (.f64 c (fma.f64 b c a)))) i)))
	39.5b	(.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))))
	28.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 c (.f64 i (fma.f64 c b a)))) (sqrt.f64 (.f64 c (*.f64 i (fma.f64 c b a)))))))

Compiler

Compiled 4398 to 1323 computations (69.9% saved)

localize13.0ms (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))))
✓	1.3b	(*.f64 i (fma.f64 c b a))
✓	4.1b	(.f64 c (.f64 i (fma.f64 c b a)))

series92.0ms (0.9%)

Counts

3 → 192

Calls

3 calls:

60.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (*.f64 i (fma.f64 c b a))))
20.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
11.0ms	(*.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))

simplify163.0ms (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	153	4703
1	336	3822
2	1163	3783
3	4522	3783
4	4977	3783
5	4931	3783

prune169.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	10	1	11
Picked	1	0	1
Done	0	1	1
Total	145	6	151

Error

0.0b

Counts

151 → 6

Alt Table

Status	Error	Program
	5.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))))
	4.6b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
	5.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 i (fma.f64 c b a)) c)))
✓	7.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
▶	2.3b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c i) (fma.f64 c b a))))
	20.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))

Compiler

Compiled 3417 to 914 computations (73.3% 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)))
✓	6.6b	(.f64 (.f64 c i) (fma.f64 c b a))

series85.0ms (0.9%)

Counts

2 → 144

Calls

2 calls:

64.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))
21.0ms	(.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 t z (.f64 y x)) (.f64 (*.f64 c i) (fma.f64 c b a)))

simplify128.0ms (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	128	3996
1	308	3155
2	1033	3116
3	3628	3108
4	4843	3108
5	4797	3108

prune83.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	104	6	110

Error

0.0b

Counts

110 → 6

Alt Table

Status	Error	Program
	5.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))))
	4.6b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
▶	2.3b	(.f64 2 (+.f64 (fma.f64 1 (fma.f64 t z (.f64 y x)) (neg.f64 (.f64 (fma.f64 c b a) (.f64 c i)))) (fma.f64 (neg.f64 (fma.f64 c b a)) (.f64 c i) (.f64 (fma.f64 c b a) (*.f64 c i)))))
	5.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 i (fma.f64 c b a)) c)))
✓	7.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	20.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))

Compiler

Compiled 2722 to 752 computations (72.4% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 (fma.f64 t z (.f64 y x)) (neg.f64 (.f64 (fma.f64 c b a) (*.f64 c i))))
✓	6.6b	(.f64 (fma.f64 c b a) (.f64 c i))
✓	50.3b	(fma.f64 (neg.f64 (fma.f64 c b a)) (.f64 c i) (.f64 (fma.f64 c b a) (*.f64 c i)))

series130.0ms (1.3%)

Counts

3 → 192

Calls

3 calls:

65.0ms

(fma.f64 1 (fma.f64 t z (*.f64 y x)) (neg.f64 (*.f64 (fma.f64 c b a) (*.f64 c i))))

45.0ms

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

20.0ms

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

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 40

Calls

3 calls:

5.0ms

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

0.0ms

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

0.0ms

(fma.f64 1 (fma.f64 t z (*.f64 y x)) (neg.f64 (*.f64 (fma.f64 c b a) (*.f64 c i))))

simplify134.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

437×	`fma-neg_binary64`
396×	`*-commutative_binary64`
324×	`unsub-neg_binary64`
309×	`distribute-rgt-in_binary64`
308×	`exp-prod_binary64`

Counts

232 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	3893
1	255	2947
2	774	2828
3	2111	2828
4	3708	2828
5	4950	2828
6	4773	2828

prune161.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	143	6	149

Error

0.0b

Counts

149 → 6

Alt Table

Status	Error	Program
	5.4b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (.f64 (cbrt.f64 i) (fma.f64 c b a))))))
	4.6b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
✓	2.3b	(.f64 2 (+.f64 (fma.f64 1 (fma.f64 t z (.f64 y x)) (neg.f64 (.f64 (fma.f64 c b a) (.f64 c i)))) (fma.f64 (neg.f64 (fma.f64 c b a)) (.f64 c i) (.f64 (fma.f64 c b a) (*.f64 c i)))))
	5.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 i (fma.f64 c b a)) c)))
✓	7.6b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i)))
	20.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 c (.f64 i (fma.f64 c b a))) 3))))

Compiler

Compiled 5909 to 1170 computations (80.2% saved)

regimes3.0s (29.6%)

Accuracy

Total 1.2b remaining (97.4%)

Threshold costs 0b (0%)

Counts

119 → 3

Compiler

Compiled 54408 to 34198 computations (37.1% saved)

bsearch5.0ms (0%)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`distribute-rgt-neg-in_binary64`
12×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	85
1	63	85
2	86	85
3	104	85
4	130	85
5	146	85
6	154	85
7	158	85
8	159	85
9	159	85

end24.0ms (0.2%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 330 to 180 computations (45.5% saved)

sample2.3s (22.7%)

Algorithm

1×

intervals

Results

644.0ms	8000×	body	128	valid
618.0ms	7247×	body	128	invalid

Compiler

Compiled 285 to 172 computations (39.6% saved)

Details

analyze2.7s (27.5%)

sample98.0ms (1%)

simplify225.0ms (2.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series100.0ms (1%)

rewrite12.0ms (0.1%)

simplify123.0ms (1.2%)

prune183.0ms (1.8%)

localize13.0ms (0.1%)

series92.0ms (0.9%)

rewrite14.0ms (0.1%)

simplify163.0ms (1.6%)

prune169.0ms (1.7%)

localize14.0ms (0.1%)

series85.0ms (0.9%)

rewrite9.0ms (0.1%)

simplify128.0ms (1.3%)

prune83.0ms (0.8%)

localize17.0ms (0.2%)

series130.0ms (1.3%)

rewrite7.0ms (0.1%)

simplify134.0ms (1.3%)

prune161.0ms (1.6%)

regimes3.0s (29.6%)

bsearch5.0ms (0%)

simplify9.0ms (0.1%)

end24.0ms (0.2%)

sample2.3s (22.7%)

Profiling