Details

analyze296.0ms (3.6%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.2s (15%)

Symmetry

(sort x y)

(sort z t)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify50.0ms (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

8.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.0b	(/.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
✓	0.5b	(-.f64 (.f64 x y) (.f64 z t))
✓	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

series41.0ms (0.5%)

Counts

2 → 108

Calls

2 calls:

30.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
11.0ms	(-.f64 (.f64 x y) (.f64 z t))

rewrite13.0ms (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)
5.0ms	(-.f64 (.f64 x y) (.f64 z t))

simplify134.0ms (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

prune148.0ms (1.8%)

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

7.4b

Counts

94 → 10

Alt Table

Status	Error	Program
	33.4b	(neg.f64 (/.f64 (*.f64 t z) a))
	8.6b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	36.0b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	8.6b	(.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))
	33.7b	(/.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))))
▶	8.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	8.2b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
	28.2b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	34.3b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
	32.9b	(/.f64 (*.f64 y x) a)

Compiler

Compiled 2024 to 509 computations (74.9% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.5b	(-.f64 (.f64 x y) (.f64 z t))
✓	7.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))

series58.0ms (0.7%)

Counts

1 → 60

Calls

1 calls:

58.0ms

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

rewrite21.0ms (0.3%)

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:

16.0ms

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

simplify151.0ms (1.8%)

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

prune202.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Error

7.4b

Counts

115 → 11

Alt Table

Status	Error	Program
▶	8.6b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	28.7b	(.f64 (/.f64 (.f64 (-.f64 (.f64 y x) (.f64 t z)) (fma.f64 t z (.f64 y x))) (fma.f64 t z (.f64 y x))) (/.f64 1 a))
	32.7b	(/.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))))
	34.3b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
	8.6b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
	33.4b	(neg.f64 (/.f64 (*.f64 t z) a))
	36.0b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
	8.6b	(.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))
✓	8.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	28.2b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	32.9b	(/.f64 (*.f64 y x) a)

Compiler

Compiled 2436 to 837 computations (65.6% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	2.7b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
✓	5.0b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))

series979.0ms (11.8%)

Counts

4 → 144

Calls

4 calls:

842.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
64.0ms	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
41.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
32.0ms	(cbrt.f64 a)

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
43×	`cbrt-prod_binary64`

Counts

4 → 156

Calls

4 calls:

11.0ms	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
11.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
7.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
1.0ms	(cbrt.f64 a)

simplify184.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
649×	`associate-/r/_binary64`
218×	`distribute-rgt-in_binary64`
204×	`distribute-lft-in_binary64`
173×	`exp-prod_binary64`

Counts

300 → 266

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	6162
1	492	5447
2	1888	5362
3	4119	5306
4	4970	5306

prune428.0ms (5.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	298	4	302
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	300	13	313

Error

7.4b

Counts

313 → 13

Alt Table

Status	Error	Program
✓	8.6b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	32.7b	(/.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))))
	28.2b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	8.7b	(/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))) (cbrt.f64 a))
	34.3b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
	8.6b	(/.f64 (/.f64 1 (cbrt.f64 a)) (/.f64 (cbrt.f64 a) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (cbrt.f64 a))))
	8.6b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
	36.0b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
▶	8.6b	(.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))
	38.6b	(/.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 (pow.f64 a 2)) 1/3) (*.f64 t z))) (cbrt.f64 a))
✓	8.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	37.2b	(/.f64 (exp.f64 (log.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))))) (cbrt.f64 a))
	32.9b	(/.f64 (*.f64 y x) a)

Compiler

Compiled 7854 to 1844 computations (76.5% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 y x) (.f64 t z))
✓	0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y x) (*.f64 t z))))
✓	1.1b	(.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))
✓	18.5b	(cbrt.f64 (-.f64 (.f64 y x) (.f64 t z)))

series314.0ms (3.8%)

Counts

4 → 168

Calls

4 calls:

133.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y x) (*.f64 t z))))
123.0ms	(cbrt.f64 (-.f64 (.f64 y x) (.f64 t z)))
48.0ms	(.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))
9.0ms	(-.f64 (.f64 y x) (.f64 t z))

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`cbrt-div_binary64`
29×	`cbrt-prod_binary64`
28×	`associate-r_binary64`
26×	`*-un-lft-identity_binary64`

Counts

4 → 144

Calls

4 calls:

18.0ms	(.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))
8.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 y x) (.f64 t z))) (cbrt.f64 (-.f64 (.f64 y x) (*.f64 t z))))
3.0ms	(-.f64 (.f64 y x) (.f64 t z))
3.0ms	(cbrt.f64 (-.f64 (.f64 y x) (.f64 t z)))

simplify199.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

789×	`associate-/l*_binary64`
284×	`fma-def_binary64`
279×	`*-commutative_binary64`
152×	`cancel-sign-sub-inv_binary64`
152×	`sub-neg_binary64`

Counts

312 → 357

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	701	12720
1	2365	11992
2	5141	11992

prune905.0ms (10.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	589	2	591
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	591	13	604

Error

7.4b

Counts

604 → 13

Alt Table

Status	Error	Program
✓	8.6b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	32.7b	(/.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))))
	28.2b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	8.7b	(/.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))))) (cbrt.f64 a))
	34.3b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
	8.6b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z t)) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
	36.0b	(/.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))))
✓	8.6b	(.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))
	38.6b	(/.f64 (.f64 -1 (.f64 (pow.f64 (/.f64 1 (pow.f64 a 2)) 1/3) (*.f64 t z))) (cbrt.f64 a))
✓	8.1b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	41.1b	(.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (pow.f64 t 2)) (.f64 2 (log.f64 (/.f64 -1 z)))))) (/.f64 (cbrt.f64 (-.f64 (.f64 y x) (*.f64 t z))) a))
	8.0b	(neg.f64 (/.f64 (-.f64 (.f64 t z) (.f64 y x)) a))
	32.9b	(/.f64 (*.f64 y x) a)

Compiler

Compiled 31800 to 11146 computations (64.9% saved)

regimes2.4s (29.3%)

Accuracy

Total 0.3b remaining (5.5%)

Threshold costs 0.3b (5.5%)

Counts

148 → 1

Compiler

Compiled 39681 to 22276 computations (43.9% saved)

simplify4.0ms (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

end334.0ms (4%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 404 to 229 computations (43.3% 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

analyze296.0ms (3.6%)

sample1.2s (15%)

simplify50.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series41.0ms (0.5%)

rewrite13.0ms (0.2%)

simplify134.0ms (1.6%)

prune148.0ms (1.8%)

localize15.0ms (0.2%)

series58.0ms (0.7%)

rewrite21.0ms (0.3%)

simplify151.0ms (1.8%)

prune202.0ms (2.4%)

localize23.0ms (0.3%)

series979.0ms (11.8%)

rewrite42.0ms (0.5%)

simplify184.0ms (2.2%)

prune428.0ms (5.2%)

localize22.0ms (0.3%)

series314.0ms (3.8%)

rewrite50.0ms (0.6%)

simplify199.0ms (2.4%)

prune905.0ms (10.9%)

regimes2.4s (29.3%)

simplify4.0ms (0%)

end334.0ms (4%)

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