Details

analyze1.8s (27.1%)

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)

sample1.7s (25.2%)

Symmetry

(sort x y)

(sort z t)

Results

1.1s	8256×	body	128	valid
447.0ms	3385×	body	128	invalid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify205.0ms (3.1%)

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

prune4.0ms (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

7.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.4b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
▶	7.4b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

Compiler

Compiled 100 to 69 computations (31% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
✓	0.2b	(.f64 (.f64 z 9) t)
✓	6.9b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

series55.0ms (0.8%)

Counts

3 → 132

Calls

3 calls:

38.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
12.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
5.0ms	(.f64 (.f64 z 9) t)

rewrite16.0ms (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:

7.0ms	(/.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))

simplify94.0ms (1.4%)

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

prune129.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Error

7.0b

Counts

117 → 12

Alt Table

Status	Error	Program
	8.2b	(.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))
	31.5b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	7.4b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
	32.3b	(.f64 (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
	7.4b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
	33.9b	(/.f64 (.f64 y x) (.f64 a 2))
	8.2b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2)))
	7.7b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	30.8b	(/.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))))
	36.2b	(.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))
	31.4b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
▶	7.4b	(/.f64 (fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t))) (*.f64 a 2))

Compiler

Compiled 2839 to 1639 computations (42.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t)))
	0.2b	(.f64 (.f64 z 9) t)
✓	6.9b	(/.f64 (fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t))) (*.f64 a 2))

series52.0ms (0.8%)

Counts

2 → 108

Calls

2 calls:

41.0ms	(/.f64 (fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t))) (*.f64 a 2))
12.0ms	(fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 33

Calls

2 calls:

3.0ms	(/.f64 (fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t))) (*.f64 a 2))
0.0ms	(fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t)))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
465×	`fma-def_binary64`
279×	`div-sub_binary64`
222×	`associate-/l*_binary64`
211×	`associate-l_binary64`

Counts

141 → 68

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	89	2397
1	210	2009
2	587	2009
3	2224	2009
4	4995	2009
5	4964	2009

prune96.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	98	12	110

Error

7.0b

Counts

110 → 12

Alt Table

Status	Error	Program
	8.2b	(.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))
	31.5b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	7.4b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
	32.3b	(.f64 (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
▶	7.4b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
	33.9b	(/.f64 (.f64 y x) (.f64 a 2))
	8.2b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2)))
	7.7b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	30.8b	(/.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))))
	36.2b	(.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))
	31.4b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
✓	7.4b	(/.f64 (fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t))) (*.f64 a 2))

Compiler

Compiled 2385 to 1486 computations (37.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
✓	0.2b	(.f64 z (.f64 9 t))
✓	6.9b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))

series56.0ms (0.8%)

Counts

3 → 132

Calls

3 calls:

40.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
11.0ms	(-.f64 (.f64 x y) (.f64 z (*.f64 9 t)))
5.0ms	(.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)))

simplify93.0ms (1.4%)

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

prune124.0ms (1.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	114	13	127

Error

7.0b

Counts

127 → 13

Alt Table

Status	Error	Program
	8.2b	(.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))
	31.5b	(.f64 -9/2 (/.f64 (.f64 t z) a))
▶	7.4b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
	32.3b	(.f64 (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) (*.f64 a 2))))
✓	7.4b	(/.f64 (-.f64 (.f64 x y) (.f64 z (.f64 9 t))) (.f64 a 2))
	33.9b	(/.f64 (.f64 y x) (.f64 a 2))
	8.2b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2)))
	31.4b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
	36.8b	(/.f64 (/.f64 (fma.f64 y (.f64 y (.f64 x x)) (.f64 (.f64 (.f64 t z) (.f64 t z)) -81)) (fma.f64 z (.f64 t 9) (.f64 y x))) (*.f64 a 2))
	7.7b	(/.f64 1 (/.f64 a (/.f64 (fma.f64 t (.f64 z -9) (.f64 y x)) 2)))
	30.8b	(/.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))))
	36.2b	(.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))
✓	7.4b	(/.f64 (fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t))) (*.f64 a 2))

Compiler

Compiled 2882 to 1654 computations (42.6% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 -9 (.f64 z t) (.f64 x y))
✓	7.0b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series55.0ms (0.8%)

Counts

2 → 108

Calls

2 calls:

43.0ms	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
12.0ms	(fma.f64 -9 (.f64 z t) (.f64 x y))

rewrite9.0ms (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))

simplify101.0ms (1.5%)

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

prune99.0ms (1.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	5	5	10
Picked	0	1	1
Done	1	1	2
Total	88	13	101

Error

7.0b

Counts

101 → 13

Alt Table

Status	Error	Program
	7.8b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	31.5b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	33.9b	(/.f64 (.f64 y x) (.f64 a 2))
	8.2b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)))) (/.f64 a (/.f64 (cbrt.f64 (fma.f64 t (.f64 z -9) (*.f64 y x))) 2)))
	33.9b	(.f64 (.f64 y x) (/.f64 1/2 a))
	31.4b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
✓	7.4b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
	8.4b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
	30.8b	(/.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))))
	8.2b	(.f64 (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
	32.3b	(.f64 (sqrt.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 1/2 a))) (sqrt.f64 (.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
	8.3b	(.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)))
✓	7.4b	(/.f64 (fma.f64 x y (neg.f64 (.f64 (.f64 z 9) t))) (*.f64 a 2))

Compiler

Compiled 1972 to 1052 computations (46.7% saved)

regimes1.5s (22.2%)

Accuracy

Total 0.4b remaining (5.8%)

Threshold costs 0.4b (5.8%)

Counts

109 → 1

Compiler

Compiled 33354 to 23026 computations (31% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`+-rgt-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	17
1	19	17
2	19	17

end347.0ms (5.3%)

Remove: (sort x y)
Compiler: Compiled 434 to 300 computations (30.9% saved)

Details

analyze1.8s (27.1%)

sample1.7s (25.2%)

simplify205.0ms (3.1%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series55.0ms (0.8%)

rewrite16.0ms (0.2%)

simplify94.0ms (1.4%)

prune129.0ms (1.9%)

localize9.0ms (0.1%)

series52.0ms (0.8%)

rewrite5.0ms (0.1%)

simplify91.0ms (1.4%)

prune96.0ms (1.4%)

localize10.0ms (0.1%)

series56.0ms (0.8%)

rewrite15.0ms (0.2%)

simplify93.0ms (1.4%)

prune124.0ms (1.9%)

localize10.0ms (0.2%)

series55.0ms (0.8%)

rewrite9.0ms (0.1%)

simplify101.0ms (1.5%)

prune99.0ms (1.5%)

regimes1.5s (22.2%)

simplify3.0ms (0.1%)

end347.0ms (5.3%)

Profiling