Details

analyze1.3s (22.8%)

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)

sample1.6s (29.4%)

Symmetry

(sort x y)

(sort z t)

Results

1.0s	8256×	body	128	valid
492.0ms	2998×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify43.0ms (0.8%)

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

10.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.4b	(/.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
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	9.8b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

series38.0ms (0.7%)

Counts

2 → 108

Calls

2 calls:

28.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
10.0ms	(-.f64 (.f64 x y) (.f64 z t))

rewrite11.0ms (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:

5.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
4.0ms	(-.f64 (.f64 x y) (.f64 z t))

simplify117.0ms (2.1%)

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

prune66.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	10	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Error

10.0b

Counts

94 → 10

Alt Table

Status	Error	Program
	36.0b	(neg.f64 (/.f64 (*.f64 t z) a))
	35.7b	(.f64 (sqrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (.f64 y x) (*.f64 t z))) a))
	11.2b	(.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))
	11.1b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	35.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	32.2b	(/.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))))
	11.3b	(.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)))
▶	10.5b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	10.8b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	32.4b	(/.f64 (*.f64 y x) a)

Compiler

Compiled 2034 to 507 computations (75.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	9.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))

series26.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

26.0ms

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

rewrite11.0ms (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:

8.0ms

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

simplify92.0ms (1.6%)

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

prune104.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Error

10.0b

Counts

115 → 11

Alt Table

Status	Error	Program
	36.0b	(neg.f64 (/.f64 (*.f64 t z) a))
	32.2b	(/.f64 (.f64 (-.f64 (.f64 y x) (.f64 t z)) (fma.f64 t z (.f64 y x))) (.f64 a (fma.f64 t z (.f64 y x))))
	35.7b	(.f64 (sqrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (/.f64 (sqrt.f64 (-.f64 (.f64 y x) (*.f64 t z))) a))
	36.1b	(.f64 (neg.f64 (.f64 t z)) (/.f64 1 a))
	32.4b	(.f64 (.f64 y x) (/.f64 1 a))
	11.2b	(.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))
	11.1b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	35.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	11.3b	(.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)))
▶	10.8b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	32.4b	(/.f64 (*.f64 y x) a)

Compiler

Compiled 2400 to 814 computations (66.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	0.6b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
✓	9.8b	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

series89.0ms (1.6%)

Counts

2 → 120

Calls

2 calls:

62.0ms	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))
27.0ms	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))

rewrite23.0ms (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:

9.0ms	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
4.0ms	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

simplify165.0ms (3%)

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

prune179.0ms (3.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	231	6	237
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	235	13	248

Error

9.9b

Counts

248 → 13

Alt Table

Status	Error	Program
	36.9b	(/.f64 1 (.f64 (/.f64 a (.f64 t z)) (-.f64 -1 (/.f64 (.f64 y x) (.f64 t z)))))
	36.0b	(neg.f64 (/.f64 (*.f64 t z) a))
	32.2b	(/.f64 (.f64 (-.f64 (.f64 y x) (.f64 t z)) (fma.f64 t z (.f64 y x))) (.f64 a (fma.f64 t z (.f64 y x))))
▶	10.4b	(.f64 -1 (/.f64 (-.f64 (.f64 t z) (*.f64 y x)) a))
	11.3b	(.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)))
	31.9b	(.f64 (/.f64 (.f64 (-.f64 (.f64 y x) (.f64 t z)) (fma.f64 y x (.f64 t z))) a) (/.f64 1 (fma.f64 y x (.f64 t z))))
	10.8b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (.f64 x y) (*.f64 z t)))))
	36.1b	(.f64 (neg.f64 (.f64 t z)) (/.f64 1 a))
	32.4b	(.f64 (.f64 y x) (/.f64 1 a))
	11.1b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	35.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	33.3b	(/.f64 1 (.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y x)) 1) (/.f64 a (.f64 y x))))
	32.6b	(/.f64 1 (/.f64 a (*.f64 y x)))

Compiler

Compiled 5959 to 1798 computations (69.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 t z) (.f64 y x))
✓	9.8b	(/.f64 (-.f64 (.f64 t z) (.f64 y x)) a)

series34.0ms (0.6%)

Counts

2 → 64

Calls

2 calls:

25.0ms	(/.f64 (-.f64 (.f64 t z) (.f64 y x)) a)
9.0ms	(-.f64 (.f64 t z) (.f64 y x))

rewrite11.0ms (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:

6.0ms	(/.f64 (-.f64 (.f64 t z) (.f64 y x)) a)
3.0ms	(-.f64 (.f64 t z) (.f64 y x))

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

643×	`distribute-rgt-in_binary64`
297×	`fma-neg_binary64`
267×	`associate-l_binary64`
223×	`fma-def_binary64`
209×	`associate-r_binary64`

Counts

112 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	94	1651
1	243	1571
2	739	1565
3	2331	1565
4	4551	1565
5	4970	1565
6	4912	1565

prune54.0ms (1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	65	13	78

Error

9.9b

Counts

78 → 13

Alt Table

Status	Error	Program
	36.9b	(/.f64 1 (.f64 (/.f64 a (.f64 t z)) (-.f64 -1 (/.f64 (.f64 y x) (.f64 t z)))))
	36.0b	(neg.f64 (/.f64 (*.f64 t z) a))
	32.2b	(/.f64 (.f64 (-.f64 (.f64 y x) (.f64 t z)) (fma.f64 t z (.f64 y x))) (.f64 a (fma.f64 t z (.f64 y x))))
	36.2b	(.f64 -1 (.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 t z) (.f64 y x)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 t z) (.f64 y x)) a))))
	31.9b	(.f64 (/.f64 (.f64 (-.f64 (.f64 y x) (.f64 t z)) (fma.f64 y x (.f64 t z))) a) (/.f64 1 (fma.f64 y x (.f64 t z))))
	10.8b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (.f64 x y) (*.f64 z t)))))
	36.1b	(.f64 (neg.f64 (.f64 t z)) (/.f64 1 a))
	32.4b	(.f64 (.f64 y x) (/.f64 1 a))
	11.1b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	35.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
✓	10.4b	(.f64 -1 (/.f64 (-.f64 (.f64 t z) (*.f64 y x)) a))
	33.3b	(/.f64 1 (.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y x)) 1) (/.f64 a (.f64 y x))))
	32.6b	(/.f64 1 (/.f64 a (*.f64 y x)))

Compiler

Compiled 1505 to 495 computations (67.1% saved)

regimes1.3s (23.2%)

Accuracy

Total 0.3b remaining (4.5%)

Threshold costs 0.3b (4.5%)

Counts

126 → 1

Compiler

Compiled 27337 to 16441 computations (39.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-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	11	13
1	23	13
2	31	13
3	36	13
4	38	13
5	38	13

end160.0ms (2.9%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 341 to 204 computations (40.2% 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

analyze1.3s (22.8%)

sample1.6s (29.4%)

simplify43.0ms (0.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series38.0ms (0.7%)

rewrite11.0ms (0.2%)

simplify117.0ms (2.1%)

prune66.0ms (1.2%)

localize8.0ms (0.1%)

series26.0ms (0.5%)

rewrite11.0ms (0.2%)

simplify92.0ms (1.6%)

prune104.0ms (1.9%)

localize9.0ms (0.2%)

series89.0ms (1.6%)

rewrite23.0ms (0.4%)

simplify165.0ms (3%)

prune179.0ms (3.2%)

localize8.0ms (0.2%)

series34.0ms (0.6%)

rewrite11.0ms (0.2%)

simplify103.0ms (1.9%)

prune54.0ms (1%)

regimes1.3s (23.2%)

simplify4.0ms (0.1%)

end160.0ms (2.9%)

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