Details

analyze1.2s (17.6%)

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 (21.3%)

Symmetry

(sort x y)

(sort z t)

Results

993.0ms	8256×	body	128	valid
364.0ms	3180×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify46.0ms (0.7%)

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

9.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.9b	(/.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
✓	0.2b	(-.f64 (.f64 x y) (.f64 z t))
✓	9.3b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

series34.0ms (0.5%)

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))

rewrite8.0ms (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:

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

simplify109.0ms (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

prune71.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Error

9.5b

Counts

94 → 11

Alt Table

Status	Error	Program
	10.4b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	33.7b	(/.f64 (*.f64 y x) a)
	35.9b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
	39.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	11.0b	(.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)))
	28.2b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z t) (.f64 z t))) (.f64 a (+.f64 (.f64 x y) (*.f64 z t))))
	10.8b	(.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)))
	38.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y x) (.f64 t z)) a) 3))
▶	10.2b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	10.8b	(/.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)
	35.1b	(neg.f64 (/.f64 (*.f64 t z) a))

Compiler

Compiled 2096 to 535 computations (74.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.2b	(-.f64 (.f64 x y) (.f64 z t))
✓	9.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))

series26.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

26.0ms

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

rewrite9.0ms (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:

7.0ms

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

simplify82.0ms (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

prune96.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	104	12	116

Error

9.5b

Counts

116 → 12

Alt Table

Status	Error	Program
	35.9b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
	28.2b	(/.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 a (-.f64 (.f64 x y) (.f64 z t))))
	33.7b	(/.f64 (*.f64 y x) a)
	23.4b	(/.f64 (.f64 (/.f64 (-.f64 (.f64 y x) (.f64 t z)) a) (fma.f64 t z (.f64 y x))) (+.f64 (.f64 x y) (.f64 z t)))
	39.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	36.2b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 (/.f64 1 a))) (sqrt.f64 (/.f64 1 a)))
	11.0b	(.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)))
	10.8b	(.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 (.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)
	35.1b	(neg.f64 (/.f64 (*.f64 t z) a))
	35.3b	(.f64 (neg.f64 (.f64 t z)) (/.f64 1 a))

Compiler

Compiled 2504 to 864 computations (65.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(-.f64 (.f64 x y) (.f64 z t))
✓	0.6b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
✓	9.3b	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

series82.0ms (1.2%)

Counts

2 → 120

Calls

2 calls:

57.0ms	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))
24.0ms	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))

rewrite20.0ms (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)))

simplify141.0ms (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

prune200.0ms (2.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	233	16	249

Error

9.5b

Counts

249 → 16

Alt Table

Status	Error	Program
	35.9b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
	28.2b	(/.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 a (-.f64 (.f64 x y) (.f64 z t))))
	33.7b	(/.f64 (*.f64 y x) a)
	23.4b	(/.f64 (.f64 (/.f64 (-.f64 (.f64 y x) (.f64 t z)) a) (fma.f64 t z (.f64 y x))) (+.f64 (.f64 x y) (.f64 z t)))
▶	10.8b	(/.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)
	33.7b	(/.f64 1 (/.f64 a (*.f64 y x)))
	35.1b	(neg.f64 (/.f64 (*.f64 t z) a))
	35.3b	(/.f64 1 (.f64 (/.f64 a (.f64 t z)) (-.f64 -1 (/.f64 (.f64 y x) (.f64 t z)))))
	33.9b	(/.f64 1 (/.f64 a (cbrt.f64 (pow.f64 (-.f64 (.f64 y x) (.f64 t z)) 3))))
	35.5b	(/.f64 1 (neg.f64 (/.f64 a (*.f64 t z))))
	39.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	36.2b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 (/.f64 1 a))) (sqrt.f64 (/.f64 1 a)))
	11.0b	(.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)))
	10.8b	(.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)))
	34.2b	(/.f64 1 (.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y x)) 1) (/.f64 a (.f64 y x))))

Compiler

Compiled 6123 to 1871 computations (69.4% saved)

localize11.0ms (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))))
✓	9.3b	(/.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)
✓	10.1b	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

series273.0ms (4%)

Counts

4 → 204

Calls

4 calls:

110.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
87.0ms	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))
46.0ms	(/.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)
29.0ms	(.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))))

rewrite75.0ms (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:

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))))
15.0ms	(/.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)
8.0ms	(.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)))

simplify221.0ms (3.2%)

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

prune539.0ms (7.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	655	0	655
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	655	16	671

Error

9.5b

Counts

671 → 16

Alt Table

Status	Error	Program
	35.9b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a))
	28.2b	(/.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 a (-.f64 (.f64 x y) (.f64 z t))))
	33.7b	(/.f64 (*.f64 y x) a)
	23.4b	(/.f64 (.f64 (/.f64 (-.f64 (.f64 y x) (.f64 t z)) a) (fma.f64 t z (.f64 y x))) (+.f64 (.f64 x y) (.f64 z t)))
✓	10.8b	(/.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)
	33.7b	(/.f64 1 (/.f64 a (*.f64 y x)))
	35.1b	(neg.f64 (/.f64 (*.f64 t z) a))
	35.3b	(/.f64 1 (.f64 (/.f64 a (.f64 t z)) (-.f64 -1 (/.f64 (.f64 y x) (.f64 t z)))))
	33.9b	(/.f64 1 (/.f64 a (cbrt.f64 (pow.f64 (-.f64 (.f64 y x) (.f64 t z)) 3))))
	35.5b	(/.f64 1 (neg.f64 (/.f64 a (*.f64 t z))))
	39.7b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	36.2b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (sqrt.f64 (/.f64 1 a))) (sqrt.f64 (/.f64 1 a)))
	11.0b	(.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)))
	10.8b	(.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)))
	34.2b	(/.f64 1 (.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y x)) 1) (/.f64 a (.f64 y x))))

Compiler

Compiled 36140 to 12112 computations (66.5% saved)

regimes1.9s (28.1%)

Accuracy

Total 0.3b remaining (4.2%)

Threshold costs 0.3b (4.2%)

Counts

171 → 1

Compiler

Compiled 42637 to 24560 computations (42.4% 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

end179.0ms (2.6%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 452 to 251 computations (44.5% 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 (17.6%)

sample1.5s (21.3%)

simplify46.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series34.0ms (0.5%)

rewrite8.0ms (0.1%)

simplify109.0ms (1.6%)

prune71.0ms (1%)

localize7.0ms (0.1%)

series26.0ms (0.4%)

rewrite9.0ms (0.1%)

simplify82.0ms (1.2%)

prune96.0ms (1.4%)

localize8.0ms (0.1%)

series82.0ms (1.2%)

rewrite20.0ms (0.3%)

simplify141.0ms (2.1%)

prune200.0ms (2.9%)

localize11.0ms (0.2%)

series273.0ms (4%)

rewrite75.0ms (1.1%)

simplify221.0ms (3.2%)

prune539.0ms (7.9%)

regimes1.9s (28.1%)

simplify3.0ms (0%)

end179.0ms (2.6%)

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