Details

analyze1.2s (16.2%)

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 (21.7%)

Symmetry

(sort x y)

(sort z t)

Results

1.0s	8256×	body	128	valid
518.0ms	3068×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify44.0ms (0.6%)

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)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series36.0ms (0.5%)

Counts

2 → 108

Calls

2 calls:

27.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
9.0ms	(-.f64 (.f64 x y) (.f64 z t))

rewrite10.0ms (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 → 48

Calls

2 calls:

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

simplify121.0ms (1.6%)

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

prune85.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Error

6.3b

Counts

94 → 9

Alt Table

Status	Error	Program
	7.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) a)
	31.9b	(neg.f64 (/.f64 (*.f64 t z) a))
▶	6.7b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 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)))
	7.5b	(.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))
	37.2b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	32.8b	(/.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)
	6.8b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	33.3b	(/.f64 (*.f64 y x) a)

Compiler

Compiled 2014 to 481 computations (76.1% 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))
✓	6.3b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))

series29.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

29.0ms

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

rewrite11.0ms (0.1%)

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 (1.2%)

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

prune83.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	104	10	114

Error

6.3b

Counts

114 → 10

Alt Table

Status	Error	Program
	7.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) a)
	31.9b	(neg.f64 (/.f64 (*.f64 t z) a))
	33.3b	(.f64 (.f64 y x) (/.f64 1 a))
✓	6.7b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 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 (neg.f64 (.f64 t z)) (/.f64 1 a))
	32.8b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 y x) (*.f64 t z)) 3)) (/.f64 1 a))
	7.5b	(.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))
▶	6.8b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	33.3b	(/.f64 (*.f64 y x) a)

Compiler

Compiled 2326 to 785 computations (66.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
✓	6.3b	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

series91.0ms (1.2%)

Counts

2 → 120

Calls

2 calls:

63.0ms	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))
28.0ms	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))

rewrite25.0ms (0.3%)

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

simplify164.0ms (2.1%)

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

prune201.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	233	4	237
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	236	11	247

Error

6.3b

Counts

247 → 11

Alt Table

Status	Error	Program
	36.5b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))) (sqrt.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t)))))
	33.4b	(/.f64 1 (/.f64 a (*.f64 y x)))
▶	7.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) a)
	31.9b	(neg.f64 (/.f64 (*.f64 t z) a))
✓	6.7b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 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 (neg.f64 (.f64 t z)) (/.f64 1 a))
	32.8b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 y x) (*.f64 t z)) 3)) (/.f64 1 a))
	32.7b	(/.f64 1 (.f64 (/.f64 a (.f64 t z)) (-.f64 -1 (/.f64 (.f64 y x) (.f64 t z)))))
	33.3b	(/.f64 (*.f64 y x) a)
	33.8b	(/.f64 1 (.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y x)) 1) (/.f64 a (.f64 y x))))

Compiler

Compiled 5857 to 1737 computations (70.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))
✓	0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	6.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) a)
✓	7.1b	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

series316.0ms (4.2%)

Counts

4 → 204

Calls

4 calls:

137.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
96.0ms	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))
49.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) a)
33.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))

rewrite82.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-div_binary64`
61×	`flip--_binary64`
61×	`flip3--_binary64`
60×	`frac-times_binary64`
30×	`associate-*l/_binary64`

Counts

4 → 180

Calls

4 calls:

17.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) a)
16.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))
9.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
2.0ms	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

simplify235.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

775×	`associate-/l*_binary64`
281×	`fma-def_binary64`
275×	`*-commutative_binary64`
155×	`sub-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`

Counts

384 → 449

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	703	14360
1	2290	13632
2	5095	13632

prune529.0ms (7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	654	1	655
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	654	12	666

Error

6.3b

Counts

666 → 12

Alt Table

Status	Error	Program
	36.5b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))) (sqrt.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t)))))
	33.4b	(/.f64 1 (/.f64 a (*.f64 y x)))
✓	7.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) a)
	31.9b	(neg.f64 (/.f64 (*.f64 t z) a))
✓	6.7b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 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 (neg.f64 (.f64 t z)) (/.f64 1 a))
	32.8b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 y x) (*.f64 t z)) 3)) (/.f64 1 a))
	37.7b	(/.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) a)
	32.7b	(/.f64 1 (.f64 (/.f64 a (.f64 t z)) (-.f64 -1 (/.f64 (.f64 y x) (.f64 t z)))))
	33.3b	(/.f64 (*.f64 y x) a)
	33.8b	(/.f64 1 (.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y x)) 1) (/.f64 a (.f64 y x))))

Compiler

Compiled 36062 to 12060 computations (66.6% saved)

regimes2.4s (31.2%)

Accuracy

Total 0.3b remaining (4.2%)

Threshold costs 0.3b (4.2%)

Counts

198 → 1

Compiler

Compiled 48696 to 29155 computations (40.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	15	16
2	22	16
3	32	16
4	39	16
5	44	16
6	46	16
7	46	16

end155.0ms (2%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 374 to 199 computations (46.8% 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

analyze1.2s (16.2%)

sample1.6s (21.7%)

simplify44.0ms (0.6%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series36.0ms (0.5%)

rewrite10.0ms (0.1%)

simplify121.0ms (1.6%)

prune85.0ms (1.1%)

localize8.0ms (0.1%)

series29.0ms (0.4%)

rewrite11.0ms (0.1%)

simplify92.0ms (1.2%)

prune83.0ms (1.1%)

localize8.0ms (0.1%)

series91.0ms (1.2%)

rewrite25.0ms (0.3%)

simplify164.0ms (2.1%)

prune201.0ms (2.6%)

localize12.0ms (0.2%)

series316.0ms (4.2%)

rewrite82.0ms (1.1%)

simplify235.0ms (3.1%)

prune529.0ms (7%)

regimes2.4s (31.2%)

simplify3.0ms (0%)

end155.0ms (2%)

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