Details

analyze2.1s (26.6%)

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 (1.5%)

Algorithm

1×

intervals

Symmetry

(sort x y)

(sort z t)

Results

20.0ms	256×	body	128	valid
14.0ms	213×	body	128	invalid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify199.0ms (2.5%)

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

7.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.1b	(.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	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.1b	(*.f64 c (fma.f64 b c a))
✓	9.0b	(.f64 (.f64 c (fma.f64 b c a)) i)

series108.0ms (1.4%)

Counts

4 → 228

Calls

4 calls:

68.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c (fma.f64 b c a)) i))
21.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
11.0ms	(fma.f64 x y (*.f64 z t))
9.0ms	(*.f64 c (fma.f64 b c a))

rewrite14.0ms (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:

4.0ms	(*.f64 c (fma.f64 b c a))
4.0ms	(.f64 (.f64 c (fma.f64 b c a)) i)
2.0ms	(-.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))

simplify113.0ms (1.4%)

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

prune163.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	150	10	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	10	161

Error

0.0b

Counts

161 → 10

Alt Table

Status	Error	Program
	33.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (*.f64 (fma.f64 c b a) (sqrt.f64 i))) (sqrt.f64 i))))
▶	5.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	7.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 (.f64 c (fma.f64 b c a)) (.f64 (cbrt.f64 i) (cbrt.f64 i))) (cbrt.f64 i))))
	12.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
	10.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i)))
	7.4b	(.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)))
	23.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	28.9b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (sqrt.f64 (.f64 (.f64 c (fma.f64 b c a)) i)) (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)))))
	22.7b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 c (fma.f64 b c a)) i) (.f64 (.f64 c (fma.f64 b c a)) i)) (.f64 (.f64 c (fma.f64 b c a)) i)))))
	7.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 4261 to 1249 computations (70.7% saved)

localize13.0ms (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 i (fma.f64 c b a))))
	0.0b	(fma.f64 x y (*.f64 z t))
✓	1.1b	(*.f64 i (fma.f64 c b a))
✓	5.1b	(.f64 c (.f64 i (fma.f64 c b a)))

series90.0ms (1.1%)

Counts

3 → 192

Calls

3 calls:

58.0ms	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a))))
17.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
15.0ms	(*.f64 i (fma.f64 c b a))

rewrite12.0ms (0.2%)

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))

simplify134.0ms (1.7%)

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

prune158.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	163	7	170

Error

Counts

170 → 7

Alt Table

Status	Error	Program
	23.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	8.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
✓	5.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	12.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
▶	2.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
	6.1b	(.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))))))
	7.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 3934 to 1052 computations (73.3% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 x y (.f64 z t)) (.f64 (*.f64 c i) (fma.f64 c b a)))
	0.0b	(fma.f64 x y (*.f64 z t))
✓	5.8b	(.f64 (.f64 c i) (fma.f64 c b a))

series80.0ms (1%)

Counts

2 → 144

Calls

2 calls:

60.0ms	(-.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)))

simplify121.0ms (1.5%)

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

prune103.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	126	7	133

Error

Counts

133 → 7

Alt Table

Status	Error	Program
	23.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	8.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
✓	5.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	12.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
✓	2.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
▶	6.1b	(.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))))))
	7.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 3178 to 866 computations (72.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 c)
	1.1b	(*.f64 i (fma.f64 c b a))
✓	2.1b	(.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a)))
✓	3.3b	(.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a))))

series390.0ms (4.9%)

Counts

3 → 108

Calls

3 calls:

332.0ms	(.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a)))
29.0ms	(.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a))))
29.0ms	(cbrt.f64 c)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64`
29×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

3 → 78

Calls

3 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a))))
4.0ms	(.f64 (cbrt.f64 c) (.f64 i (fma.f64 c b a)))
1.0ms	(cbrt.f64 c)

simplify178.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

598×	`*-commutative_binary64`
498×	`distribute-rgt-in_binary64`
486×	`distribute-lft-in_binary64`
350×	`exp-prod_binary64`
302×	`associate-l_binary64`

Counts

186 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	153	3100
1	313	2443
2	1164	2422
3	3372	2206
4	4720	2206
5	4998	2206
6	4932	2206

prune264.0ms (3.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	189	7	196

Error

Counts

196 → 7

Alt Table

Status	Error	Program
	23.3b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (cbrt.f64 (pow.f64 (.f64 c (fma.f64 c b a)) 3)) i)))
	8.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))))
✓	5.8b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a)))))
	12.4b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (+.f64 (.f64 (pow.f64 c 2) (.f64 i b)) (.f64 c (.f64 i a)))))
✓	2.1b	(.f64 2 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c i) (fma.f64 c b a))))
✓	6.1b	(.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))))))
	7.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (.f64 c (fma.f64 b c a)) i)))

Compiler

Compiled 5662 to 1406 computations (75.2% saved)

regimes1.4s (17.3%)

Accuracy

Total 0.8b remaining (96.8%)

Threshold costs 0.8b (96.8%)

Counts

61 → 3

Compiler

Compiled 24098 to 16121 computations (33.1% saved)

bsearch2.0ms (0%)

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

simplify7.0ms (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	35	91
1	62	91
2	85	91
3	103	91
4	129	91
5	145	91
6	153	91
7	157	91
8	158	91
9	158	91

end22.0ms (0.3%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 350 to 175 computations (50% saved)

sample2.1s (26.2%)

Algorithm

1×

intervals

Results

597.0ms	8000×	body	128	valid
508.0ms	7006×	body	128	invalid

Compiler

Compiled 299 to 186 computations (37.8% saved)

Details

analyze2.1s (26.6%)

sample121.0ms (1.5%)

simplify199.0ms (2.5%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series108.0ms (1.4%)

rewrite14.0ms (0.2%)

simplify113.0ms (1.4%)

prune163.0ms (2.1%)

localize13.0ms (0.2%)

series90.0ms (1.1%)

rewrite12.0ms (0.2%)

simplify134.0ms (1.7%)

prune158.0ms (2%)

localize12.0ms (0.2%)

series80.0ms (1%)

rewrite9.0ms (0.1%)

simplify121.0ms (1.5%)

prune103.0ms (1.3%)

localize15.0ms (0.2%)

series390.0ms (4.9%)

rewrite19.0ms (0.2%)

simplify178.0ms (2.3%)

prune264.0ms (3.3%)

regimes1.4s (17.3%)

bsearch2.0ms (0%)

simplify7.0ms (0.1%)

end22.0ms (0.3%)

sample2.1s (26.2%)

Profiling