Details

analyze559.0ms (6.6%)

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 19 to 14 computations (26.3% saved)

sample1.5s (17.3%)

Symmetry

(sort x y)

(sort z t)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify243.0ms (2.9%)

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

prune6.0ms (0.1%)

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

8.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.1b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
▶	8.0b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

Compiler

Compiled 100 to 69 computations (31% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 z 9) t)
✓	0.5b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
✓	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

series55.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

37.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
13.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
5.0ms	(.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:

6.0ms	(/.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))

simplify98.0ms (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

prune153.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	106	9	115
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	107	10	117

Error

7.3b

Counts

117 → 10

Alt Table

Status	Error	Program
	45.9b	(/.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))))))
▶	8.1b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
	8.1b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
	32.9b	(.f64 1/2 (/.f64 (.f64 y x) a))
	33.3b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	8.2b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	36.1b	(/.f64 (-.f64 (.f64 x y) (.f64 (sqrt.f64 (.f64 (.f64 z 9) t)) (sqrt.f64 (.f64 (.f64 z 9) t)))) (*.f64 a 2))
	8.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 2))
	36.0b	(.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))
	8.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))

Compiler

Compiled 2805 to 1611 computations (42.6% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 z (.f64 9 t))
✓	0.5b	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
✓	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))

series73.0ms (0.9%)

Counts

3 → 132

Calls

3 calls:

53.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
15.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
5.0ms	(.f64 z (.f64 9 t))

rewrite29.0ms (0.3%)

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:

9.0ms	(.f64 z (.f64 9 t))
9.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
6.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))

simplify126.0ms (1.5%)

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

prune241.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	116	9	125

Error

7.3b

Counts

125 → 9

Alt Table

Status	Error	Program
	32.9b	(.f64 1/2 (/.f64 (.f64 y x) a))
	33.3b	(.f64 -9/2 (/.f64 (.f64 t z) a))
▶	8.1b	(.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (/.f64 1/2 a))
	8.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x)))) a) (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 2))
	45.9b	(/.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))))))
	8.2b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	36.1b	(/.f64 (-.f64 (.f64 x y) (.f64 (sqrt.f64 (.f64 (.f64 z 9) t)) (sqrt.f64 (.f64 (.f64 z 9) t)))) (*.f64 a 2))
	36.0b	(.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))
	8.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))

Compiler

Compiled 2782 to 1588 computations (42.9% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(.f64 z (.f64 9 t))
	0.5b	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
✓	7.5b	(.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (/.f64 1/2 a))

series71.0ms (0.8%)

Counts

1 → 60

Calls

1 calls:

70.0ms

(*.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (/.f64 1/2 a))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 38

Calls

1 calls:

13.0ms

(*.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (/.f64 1/2 a))

simplify145.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

513×	`div-sub_binary64`
336×	`*-commutative_binary64`
326×	`fma-def_binary64`
253×	`fma-neg_binary64`
245×	`associate-*r/_binary64`

Counts

98 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	2081
1	326	1792
2	1280	1789
3	3590	1789
4	4602	1789
5	5456	1789

prune201.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	135	11	146

Error

7.3b

Counts

146 → 11

Alt Table

Status	Error	Program
	32.9b	(.f64 1/2 (/.f64 (.f64 y x) a))
	33.3b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	45.9b	(/.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))))))
▶	8.2b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	36.1b	(/.f64 (-.f64 (.f64 x y) (.f64 (sqrt.f64 (.f64 (.f64 z 9) t)) (sqrt.f64 (.f64 (.f64 z 9) t)))) (*.f64 a 2))
✓	8.1b	(.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (/.f64 1/2 a))
	38.9b	(/.f64 (.f64 1/2 (fma.f64 y (.f64 y (.f64 x x)) (.f64 (.f64 (.f64 t z) (.f64 t z)) -81))) (.f64 a (fma.f64 z (.f64 t 9) (.f64 y x))))
	36.0b	(.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))
	34.3b	(.f64 (.f64 (fma.f64 z (.f64 t -9) (.f64 y x)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
	8.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
	8.6b	(.f64 (.f64 (fma.f64 z (.f64 t -9) (.f64 y x)) (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))) (/.f64 (cbrt.f64 1/2) a))

Compiler

Compiled 3403 to 1952 computations (42.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)
✓	0.3b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
✓	0.6b	(fma.f64 t (.f64 z -9) (.f64 y x))
✓	7.6b	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))

series185.0ms (2.2%)

Counts

4 → 216

Calls

4 calls:

89.0ms	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))
44.0ms	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
35.0ms	(/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)
15.0ms	(fma.f64 t (.f64 z -9) (.f64 y x))

rewrite115.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

480×	`times-frac_binary64`
239×	`*-un-lft-identity_binary64`
239×	`add-sqr-sqrt_binary64`
239×	`add-cube-cbrt_binary64`
60×	`associate-/r*_binary64`

Counts

4 → 317

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
7.0ms	(/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2))
4.0ms	(/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)
1.0ms	(fma.f64 t (.f64 z -9) (.f64 y x))

simplify541.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

410×	`fma-def_binary64`
376×	`fma-neg_binary64`
307×	`associate-/r/_binary64`
236×	`times-frac_binary64`
226×	`*-commutative_binary64`

Counts

533 → 537

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	388	15766
1	955	14652
2	3365	14501
3	4696	14489
4	4957	14489

prune894.0ms (10.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	534	3	537
Fresh	5	4	9
Picked	0	1	1
Done	0	1	1
Total	539	9	548

Error

7.3b

Counts

548 → 9

Alt Table

Status	Error	Program
	32.9b	(.f64 1/2 (/.f64 (.f64 y x) a))
	33.3b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	36.0b	(/.f64 (/.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 1))) (/.f64 a (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 2)))
✓	8.2b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	36.1b	(/.f64 (-.f64 (.f64 x y) (.f64 (sqrt.f64 (.f64 (.f64 z 9) t)) (sqrt.f64 (.f64 (.f64 z 9) t)))) (*.f64 a 2))
✓	8.1b	(.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (/.f64 1/2 a))
	7.9b	(.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (/.f64 (fma.f64 y x (.f64 (*.f64 t z) -9)) a) (sqrt.f64 2)))
	8.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) 2)) (cbrt.f64 (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) 2))) (/.f64 (cbrt.f64 (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) 2)) a))
	8.6b	(.f64 (.f64 (fma.f64 z (.f64 t -9) (.f64 y x)) (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))) (/.f64 (cbrt.f64 1/2) a))

Compiler

Compiled 15949 to 9467 computations (40.6% saved)

regimes3.0s (35.6%)

Accuracy

Total 0.4b remaining (7.3%)

Threshold costs 0.4b (7.3%)

Counts

188 → 1

Compiler

Compiled 52466 to 37726 computations (28.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	25	17
2	40	17
3	47	17
4	51	17
5	52	17
6	51	17

end190.0ms (2.2%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 312 to 224 computations (28.2% saved)

Details

analyze559.0ms (6.6%)

sample1.5s (17.3%)

simplify243.0ms (2.9%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

series55.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify98.0ms (1.1%)

prune153.0ms (1.8%)

localize12.0ms (0.1%)

series73.0ms (0.9%)

rewrite29.0ms (0.3%)

simplify126.0ms (1.5%)

prune241.0ms (2.8%)

localize17.0ms (0.2%)

series71.0ms (0.8%)

rewrite19.0ms (0.2%)

simplify145.0ms (1.7%)

prune201.0ms (2.4%)

localize11.0ms (0.1%)

series185.0ms (2.2%)

rewrite115.0ms (1.3%)

simplify541.0ms (6.4%)

prune894.0ms (10.5%)

regimes3.0s (35.6%)

simplify3.0ms (0%)

end190.0ms (2.2%)

Profiling