Details

analyze1.4s (24.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
16.4%	83.4%	0.2%	11
19.9%	79.9%	0.2%	12
21.6%	77.2%	1.2%	13
24.8%	73.7%	1.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.5s (26.9%)

Symmetry

(sort x y)

(sort z t)

Results

1.0s	8256×	body	128	valid
388.0ms	3136×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
389×	`fma-neg_binary64`
130×	`cancel-sign-sub-inv_binary64`
113×	`distribute-rgt-in_binary64`
103×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	42	13
3	73	13
4	144	13
5	223	13
6	319	13
7	495	13
8	678	13
9	833	13
10	889	13
11	976	13
12	982	13
13	987	13
14	914	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

6.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.6b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(-.f64 (.f64 x y) (.f64 z t))
✓	6.2b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

series33.0ms (0.6%)

Counts

2 → 108

Calls

2 calls:

24.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
9.0ms	(-.f64 (.f64 x y) (.f64 z t))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

4.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
2.0ms	(-.f64 (.f64 x y) (.f64 z t))

simplify113.0ms (2%)

Algorithm

1×	egg-herbie

Rules

644×	`distribute-rgt-in_binary64`
301×	`fma-neg_binary64`
270×	`associate-l_binary64`
223×	`fma-def_binary64`
213×	`associate-r_binary64`

Counts

156 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	2115
1	251	2035
2	743	2029
3	2355	2029
4	4590	2029
5	4996	2029
6	4923	2029

prune77.0ms (1.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	79	14	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	14	94

Error

6.3b

Counts

94 → 14

Alt Table

Status	Error	Program
▶	6.6b	(/.f64 (fma.f64 x y (neg.f64 (*.f64 z t))) a)
	6.7b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	32.0b	(/.f64 (*.f64 y x) a)
	35.0b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (-.f64 (.f64 x y) (.f64 z t))) (-.f64 (.f64 x y) (.f64 z t)))) a)
	30.2b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z t) (.f64 z t))) (.f64 a (fma.f64 t z (.f64 y x))))
	7.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))) (cbrt.f64 a)))
	35.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) a)))
	7.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	40.8b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (.f64 a (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t))))))
	6.7b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	33.7b	(neg.f64 (/.f64 (*.f64 t z) a))
	35.5b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
	7.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) a))
	32.4b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))

Compiler

Compiled 2286 to 615 computations (73.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))
✓	6.2b	(/.f64 (fma.f64 x y (neg.f64 (*.f64 z t))) a)

series34.0ms (0.6%)

Counts

2 → 108

Calls

2 calls:

25.0ms	(/.f64 (fma.f64 x y (neg.f64 (*.f64 z t))) a)
9.0ms	(fma.f64 x y (neg.f64 (*.f64 z t)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x y (neg.f64 (*.f64 z t))) a)
0.0ms	(fma.f64 x y (neg.f64 (*.f64 z t)))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

630×	`associate-/l*_binary64`
488×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
303×	`fma-def_binary64`
276×	`associate-/l/_binary64`

Counts

147 → 78

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	1949
1	143	1872
2	347	1872
3	1106	1872
4	4648	1872
5	4956	1872

prune55.0ms (1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	78	14	92

Error

6.3b

Counts

92 → 14

Alt Table

Status	Error	Program
✓	6.6b	(/.f64 (fma.f64 x y (neg.f64 (*.f64 z t))) a)
	6.7b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	32.0b	(/.f64 (*.f64 y x) a)
	35.0b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (-.f64 (.f64 x y) (.f64 z t))) (-.f64 (.f64 x y) (.f64 z t)))) a)
	30.2b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z t) (.f64 z t))) (.f64 a (fma.f64 t z (.f64 y x))))
	7.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))) (cbrt.f64 a)))
	35.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) a)))
	7.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	40.8b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (.f64 a (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t))))))
▶	6.7b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	33.7b	(neg.f64 (/.f64 (*.f64 t z) a))
	35.5b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
	7.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) a))
	32.4b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))

Compiler

Compiled 1960 to 534 computations (72.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(-.f64 (.f64 x y) (.f64 z t))
✓	6.3b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))

series25.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

25.0ms

(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 42

Calls

1 calls:

7.0ms

(*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (/.f64 1 a))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-l_binary64`
488×	`fma-neg_binary64`
416×	`associate-r_binary64`
344×	`distribute-lft-neg-out_binary64`
344×	`distribute-rgt-neg-out_binary64`

Counts

102 → 73

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	92	1553
1	243	1454
2	777	1454
3	2712	1454
4	4976	1454
5	5217	1454

prune87.0ms (1.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	105	14	119

Error

6.3b

Counts

119 → 14

Alt Table

Status	Error	Program
✓	6.6b	(/.f64 (fma.f64 x y (neg.f64 (*.f64 z t))) a)
▶	6.7b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	32.0b	(/.f64 (*.f64 y x) a)
	35.0b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (-.f64 (.f64 x y) (.f64 z t))) (-.f64 (.f64 x y) (.f64 z t)))) a)
	30.2b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z t) (.f64 z t))) (.f64 a (fma.f64 t z (.f64 y x))))
	7.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))) (cbrt.f64 a)))
	35.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) a)))
	7.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	31.1b	(/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z t) (.f64 z t))) (/.f64 1 a)) (+.f64 (.f64 x y) (*.f64 z t)))
	33.8b	(.f64 (neg.f64 (.f64 t z)) (/.f64 1 a))
	32.0b	(.f64 (.f64 y x) (/.f64 1 a))
	35.5b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
	7.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) a))
	32.4b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))

Compiler

Compiled 2598 to 893 computations (65.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	0.3b	(-.f64 (.f64 x y) (.f64 z t))
✓	6.2b	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

series83.0ms (1.5%)

Counts

2 → 120

Calls

2 calls:

59.0ms	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))
24.0ms	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

2 → 117

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
5.0ms	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

simplify145.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
372×	`fma-neg_binary64`
341×	`times-frac_binary64`
322×	`associate-/l/_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

237 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	5987
1	558	5614
2	2374	5371
3	4849	5371
4	5107	5371

prune227.0ms (4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	235	16	251

Error

6.3b

Counts

251 → 16

Alt Table

Status	Error	Program
✓	6.6b	(/.f64 (fma.f64 x y (neg.f64 (*.f64 z t))) a)
	34.2b	(/.f64 1 (.f64 (/.f64 a (.f64 t z)) (-.f64 -1 (/.f64 (.f64 y x) (.f64 t z)))))
	32.0b	(/.f64 (*.f64 y x) a)
	6.8b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (.f64 x y) (.f64 z t))))
	33.5b	(/.f64 1 (cbrt.f64 (pow.f64 (/.f64 a (-.f64 (.f64 y x) (.f64 t z))) 3)))
	33.8b	(.f64 (neg.f64 (.f64 t z)) (/.f64 1 a))
	30.9b	(/.f64 1 (.f64 (/.f64 a (.f64 (-.f64 (.f64 y x) (.f64 t z)) (fma.f64 y x (.f64 t z)))) (+.f64 (.f64 x y) (*.f64 z t))))
	32.6b	(/.f64 1 (.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y x)) 1) (/.f64 a (.f64 y x))))
	35.5b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
	35.0b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (-.f64 (.f64 x y) (.f64 z t))) (-.f64 (.f64 x y) (.f64 z t)))) a)
	30.2b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z t) (.f64 z t))) (.f64 a (fma.f64 t z (.f64 y x))))
	7.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))) (cbrt.f64 a)))
	35.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) a)))
	7.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	32.0b	(.f64 (.f64 y x) (/.f64 1 a))
	7.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) a))

Compiler

Compiled 5802 to 1694 computations (70.8% saved)

regimes1.4s (24.1%)

Accuracy

Total 0.3b remaining (4.8%)

Threshold costs 0.3b (4.8%)

Counts

127 → 1

Compiler

Compiled 29003 to 17708 computations (38.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	27	13
3	32	13
4	34	13
5	34	13

end198.0ms (3.5%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 459 to 248 computations (46% saved)

Iter	Nodes	Cost
0	10	13
1	21	13
2	42	13
3	73	13
4	144	13
5	223	13
6	319	13
7	495	13
8	678	13
9	833	13
10	889	13
11	976	13
12	982	13
13	987	13
14	914	13

Iter	Nodes	Cost
0	10	13
1	21	13
2	42	13
3	73	13
4	144	13
5	223	13
6	319	13
7	495	13
8	678	13
9	833	13
10	889	13
11	976	13
12	982	13
13	987	13
14	914	13

Details

analyze1.4s (24.4%)

sample1.5s (26.9%)

simplify55.0ms (1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series33.0ms (0.6%)

rewrite9.0ms (0.2%)

simplify113.0ms (2%)

prune77.0ms (1.4%)

localize7.0ms (0.1%)

series34.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify86.0ms (1.5%)

prune55.0ms (1%)

localize8.0ms (0.1%)

series25.0ms (0.4%)

rewrite10.0ms (0.2%)

simplify83.0ms (1.5%)

prune87.0ms (1.5%)

localize8.0ms (0.1%)

series83.0ms (1.5%)

rewrite21.0ms (0.4%)

simplify145.0ms (2.6%)

prune227.0ms (4%)

regimes1.4s (24.1%)

simplify3.0ms (0%)

end198.0ms (3.5%)

Profiling

Iter	Nodes	Cost
0	10	13
1	21	13
2	42	13
3	73	13
4	144	13
5	223	13
6	319	13
7	495	13
8	678	13
9	833	13
10	889	13
11	976	13
12	982	13
13	987	13
14	914	13