Details

analyze1.6s (19.7%)

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
9.4%	90.4%	0.2%	11
9.4%	90.4%	0.2%	12
10.1%	89.6%	0.2%	13
20.8%	78.9%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.6s (19.5%)

Symmetry

(sort x y)

(sort z t)

Results

1.1s	8256×	body	128	valid
427.0ms	3307×	body	128	invalid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify203.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2966×	`fma-def_binary64`
757×	`fma-neg_binary64`
541×	`cancel-sign-sub-inv_binary64`
473×	`associate-/l/_binary64`
472×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	31	17
2	103	17
3	318	17
4	794	17
5	1526	17
6	2054	17
7	2281	17
8	2975	17
9	3540	17
10	3954	17
11	4158	17
12	4097	17
13	4108	17
14	4118	17
15	4462	17
16	4531	17
17	4536	17
18	4536	17
19	6474	17

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

6.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.5b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
▶	6.4b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

Compiler

Compiled 100 to 69 computations (31% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 -9 (.f64 z t) (.f64 x y))
✓	6.0b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series51.0ms (0.6%)

Counts

2 → 108

Calls

2 calls:

40.0ms	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
11.0ms	(fma.f64 -9 (.f64 z t) (.f64 x y))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
0.0ms	(fma.f64 -9 (.f64 z t) (.f64 x y))

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

937×	`fma-def_binary64`
487×	`associate-l_binary64`
418×	`associate-r_binary64`
225×	`associate-*r/_binary64`
211×	`associate-*l/_binary64`

Counts

152 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	2547
1	248	2243
2	812	2243
3	3206	2242
4	4937	2242
5	5019	2242

prune84.0ms (1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	14	90

Error

5.8b

Counts

90 → 14

Alt Table

Status	Error	Program
	36.1b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))
	36.7b	(.f64 (sqrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (.f64 (/.f64 1/2 a) (sqrt.f64 (fma.f64 y x (.f64 (.f64 t z) -9)))))
	34.1b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	29.8b	(.f64 1/2 (/.f64 (.f64 y x) a))
	7.2b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
	7.2b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
✓	6.4b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
	36.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (.f64 t z) -9/2 (.f64 1/2 (*.f64 y x))) a) 3))
	7.2b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (cbrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)))) (cbrt.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)))) (/.f64 1/2 a))
	6.7b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	7.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (cbrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)))) (.f64 (cbrt.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
▶	6.5b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
	36.7b	(.f64 (.f64 (sqrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (sqrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)))) (/.f64 1/2 a))
	29.8b	(.f64 (.f64 y x) (/.f64 1/2 a))

Compiler

Compiled 2303 to 1266 computations (45% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
✓	0.5b	(.f64 (.f64 z 9) t)
✓	5.8b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

series54.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

38.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
11.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
4.0ms	(.f64 (.f64 z 9) t)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

3 → 62

Calls

3 calls:

5.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
4.0ms	(.f64 (.f64 z 9) t)
3.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

470×	`fma-def_binary64`
445×	`*-commutative_binary64`
325×	`div-sub_binary64`
307×	`associate-/l*_binary64`
287×	`fma-neg_binary64`

Counts

194 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	2790
1	396	2561
2	1506	2551
3	4128	2551
4	5247	2551

prune136.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	3	9	12
Picked	1	0	1
Done	1	0	1
Total	116	13	129

Error

5.8b

Counts

129 → 13

Alt Table

Status	Error	Program
	40.7b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
	6.7b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	34.1b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	29.8b	(.f64 1/2 (/.f64 (.f64 y x) a))
	7.2b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
	7.2b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
	7.2b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (cbrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)))) (cbrt.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)))) (/.f64 1/2 a))
	6.7b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	30.5b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (fma.f64 t (.f64 z 9) (.f64 y x))))
▶	6.2b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
	36.1b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))
	36.7b	(.f64 (.f64 (sqrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (sqrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)))) (/.f64 1/2 a))
	29.8b	(.f64 (.f64 y x) (/.f64 1/2 a))

Compiler

Compiled 2925 to 1689 computations (42.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 z (.f64 9 t))
✓	0.3b	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
✓	5.8b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))

series54.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

39.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
11.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
4.0ms	(.f64 z (.f64 9 t))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

3 → 62

Calls

3 calls:

6.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
4.0ms	(.f64 z (.f64 9 t))
3.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))

simplify88.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

423×	`fma-def_binary64`
421×	`*-commutative_binary64`
320×	`div-sub_binary64`
286×	`associate-/l*_binary64`
251×	`fma-neg_binary64`

Counts

194 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2786
1	388	2556
2	1391	2549
3	3885	2549
4	4952	2549

prune101.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	115	13	128

Error

5.8b

Counts

128 → 13

Alt Table

Status	Error	Program
	40.7b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
▶	6.7b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	34.1b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	29.8b	(.f64 1/2 (/.f64 (.f64 y x) a))
	36.7b	(.f64 (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2))
	7.2b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
	7.2b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
	7.2b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (cbrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)))) (cbrt.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)))) (/.f64 1/2 a))
	6.7b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	30.5b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t))) (.f64 (.f64 a 2) (fma.f64 t (.f64 z 9) (.f64 y x))))
✓	6.2b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
	36.1b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 a)))
	29.8b	(.f64 (.f64 y x) (/.f64 1/2 a))

Compiler

Compiled 2918 to 1679 computations (42.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 t (.f64 z -9) (.f64 y x))
✓	0.4b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
✓	5.8b	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))

series123.0ms (1.5%)

Counts

3 → 168

Calls

3 calls:

73.0ms	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))
39.0ms	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
10.0ms	(fma.f64 t (.f64 z -9) (.f64 y x))

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

471×	`times-frac_binary64`
230×	`*-un-lft-identity_binary64`
230×	`add-sqr-sqrt_binary64`
230×	`add-cube-cbrt_binary64`
57×	`associate-/r*_binary64`

Counts

3 → 288

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
5.0ms	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))
0.0ms	(fma.f64 t (.f64 z -9) (.f64 y x))

simplify317.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-neg_binary64`
404×	`fma-def_binary64`
296×	`associate-/r/_binary64`
234×	`times-frac_binary64`
223×	`*-commutative_binary64`

Counts

456 → 479

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	376	14401
1	938	13425
2	3317	13274
3	4740	13262
4	5054	13262

prune446.0ms (5.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	472	7	479
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	478	14	492

Error

5.8b

Counts

492 → 14

Alt Table

Status	Error	Program
	34.1b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	34.2b	(/.f64 1 (.f64 -2/9 (/.f64 a (.f64 t z))))
	6.7b	(.f64 (/.f64 1 a) (/.f64 1 (/.f64 1 (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) 2))))
	36.0b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (.f64 2 (sqrt.f64 a))))
	7.1b	(/.f64 1 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (*.f64 y x)) (sqrt.f64 2)))))
	35.8b	(/.f64 1 (fma.f64 2 (/.f64 a (.f64 y x)) (.f64 18 (/.f64 (.f64 a (.f64 t z)) (.f64 (.f64 y x) (*.f64 y x))))))
	7.2b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
	7.2b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
	40.7b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 (.f64 z 9) t) 3)) (.f64 (.f64 a 2) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 (.f64 z 9) t) (.f64 (.f64 z 9) t)) (.f64 (.f64 x y) (.f64 (*.f64 z 9) t))))))
✓	6.2b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
	38.2b	(/.f64 1 (fma.f64 (/.f64 (.f64 a (.f64 y x)) (.f64 (.f64 t z) (.f64 t z))) -2/81 (.f64 -2/9 (/.f64 a (*.f64 t z)))))
	29.8b	(.f64 (.f64 y x) (/.f64 1/2 a))
	29.9b	(/.f64 1 (.f64 2 (/.f64 a (.f64 y x))))
	6.7b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))

Compiler

Compiled 14754 to 8741 computations (40.8% saved)

regimes2.8s (34.2%)

Accuracy

Total 0.4b remaining (5.6%)

Threshold costs 0.4b (5.6%)

Counts

194 → 1

Compiler

Compiled 55495 to 39652 computations (28.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	16	17
2	16	17

end204.0ms (2.5%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 430 to 299 computations (30.5% saved)

Details

analyze1.6s (19.7%)

sample1.6s (19.5%)

simplify203.0ms (2.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series51.0ms (0.6%)

rewrite8.0ms (0.1%)

simplify98.0ms (1.2%)

prune84.0ms (1%)

localize9.0ms (0.1%)

series54.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify86.0ms (1.1%)

prune136.0ms (1.7%)

localize8.0ms (0.1%)

series54.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify88.0ms (1.1%)

prune101.0ms (1.2%)

localize9.0ms (0.1%)

series123.0ms (1.5%)

rewrite56.0ms (0.7%)

simplify317.0ms (3.9%)

prune446.0ms (5.4%)

regimes2.8s (34.2%)

simplify2.0ms (0%)

end204.0ms (2.5%)

Profiling