Details

analyze1.5s (24.8%)

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 (29.1%)

Symmetry

(sort x y)

(sort z t)

Results

1.3s	8256×	body	128	valid
395.0ms	3228×	body	128	invalid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify206.0ms (3.4%)

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))
	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

Compiler

Compiled 100 to 69 computations (31% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.6b	(fma.f64 -9 (.f64 z t) (.f64 x y))
✓	6.8b	(.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series49.0ms (0.8%)

Counts

2 → 108

Calls

2 calls:

38.0ms	(.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))

simplify100.0ms (1.7%)

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

prune101.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	77	13	90

Error

6.9b

Counts

90 → 13

Alt Table

Status	Error	Program
	7.6b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	8.1b	(.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 1/2 a))) (cbrt.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (/.f64 1/2 a)))) (cbrt.f64 (.f64 (fma.f64 -9 (.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
	33.3b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 y x (.f64 (*.f64 t z) -9)) 3)) (/.f64 1/2 a))
	36.5b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
▶	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
	8.1b	(.f64 (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
	33.1b	(.f64 (.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
	8.1b	(.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)))
	32.2b	(.f64 (.f64 y x) (/.f64 1/2 a))
	33.1b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	32.1b	(.f64 1/2 (/.f64 (.f64 y x) a))
	8.1b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
	36.5b	(.f64 (sqrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (.f64 (sqrt.f64 (fma.f64 -9 (.f64 z t) (.f64 x y))) (/.f64 1/2 a)))

Compiler

Compiled 2246 to 1244 computations (44.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (.f64 z 9) t)
✓	0.5b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
✓	6.7b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

series55.0ms (0.9%)

Counts

3 → 132

Calls

3 calls:

39.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
10.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
6.0ms	(.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))
5.0ms	(.f64 (.f64 z 9) t)
3.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

simplify91.0ms (1.5%)

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

prune107.0ms (1.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	116	12	128

Error

6.9b

Counts

128 → 12

Alt Table

Status	Error	Program
	33.1b	(.f64 (.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
	7.7b	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (.f64 x y) (.f64 (.f64 z 9) t))))
✓	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
	8.1b	(.f64 (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
	30.1b	(/.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))))
	7.6b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	32.2b	(.f64 (.f64 y x) (/.f64 1/2 a))
	33.1b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	32.1b	(.f64 1/2 (/.f64 (.f64 y x) a))
	36.5b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
	8.1b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
▶	7.2b	(/.f64 (fma.f64 x y (.f64 (.f64 t z) -9)) (*.f64 a 2))

Compiler

Compiled 2727 to 1582 computations (42% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 x y (.f64 (.f64 t z) -9))
✓	0.3b	(.f64 (.f64 t z) -9)
✓	6.7b	(/.f64 (fma.f64 x y (.f64 (.f64 t z) -9)) (*.f64 a 2))

series53.0ms (0.9%)

Counts

3 → 132

Calls

3 calls:

38.0ms	(/.f64 (fma.f64 x y (.f64 (.f64 t z) -9)) (*.f64 a 2))
10.0ms	(fma.f64 x y (.f64 (.f64 t z) -9))
5.0ms	(.f64 (.f64 t z) -9)

rewrite9.0ms (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 → 53

Calls

3 calls:

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

simplify118.0ms (2%)

Algorithm

1×	egg-herbie

Rules

377×	`distribute-rgt-in_binary64`
327×	`div-sub_binary64`
307×	`fma-def_binary64`
261×	`associate-/l*_binary64`
248×	`*-commutative_binary64`

Counts

185 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	123	2617
1	279	2353
2	907	2353
3	2487	2353
4	4983	2353

prune79.0ms (1.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	86	12	98

Error

6.8b

Counts

98 → 12

Alt Table

Status	Error	Program
	7.6b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	36.7b	(/.f64 (sqrt.f64 (fma.f64 x y (.f64 (.f64 t z) -9))) (/.f64 a (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 2)))
✓	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
	8.1b	(.f64 (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
	30.1b	(/.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))))
▶	7.4b	(/.f64 1 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 (*.f64 t z) -9))))
	33.1b	(.f64 (.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
	32.2b	(.f64 (.f64 y x) (/.f64 1/2 a))
	33.1b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	32.1b	(.f64 1/2 (/.f64 (.f64 y x) a))
	36.5b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
	8.1b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))

Compiler

Compiled 2053 to 1201 computations (41.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 x y (.f64 (.f64 t z) -9))
	0.3b	(.f64 (.f64 t z) -9)
✓	0.4b	(/.f64 1 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 (*.f64 t z) -9))))
✓	6.7b	(/.f64 (.f64 a 2) (fma.f64 x y (.f64 (*.f64 t z) -9)))

series122.0ms (2%)

Counts

2 → 120

Calls

2 calls:

83.0ms	(/.f64 (.f64 a 2) (fma.f64 x y (.f64 (*.f64 t z) -9)))
38.0ms	(/.f64 1 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 (*.f64 t z) -9))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
28×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 81

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 (*.f64 t z) -9))))
3.0ms	(/.f64 (.f64 a 2) (fma.f64 x y (.f64 (*.f64 t z) -9)))

simplify115.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

531×	`associate-/r/_binary64`
478×	`associate-/l/_binary64`
407×	`fma-def_binary64`
240×	`times-frac_binary64`
178×	`associate-/l*_binary64`

Counts

201 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	5770
1	619	5342
2	2383	5293
3	5001	5293

prune183.0ms (3.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	187	6	193
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	190	15	205

Error

6.8b

Counts

205 → 15

Alt Table

Status	Error	Program
	7.6b	(.f64 (.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
	36.7b	(/.f64 (sqrt.f64 (fma.f64 x y (.f64 (.f64 t z) -9))) (/.f64 a (/.f64 (sqrt.f64 (fma.f64 t (.f64 z -9) (.f64 y x))) 2)))
	35.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 2 (/.f64 a (fma.f64 y x (.f64 (.f64 t z) -9)))))) (/.f64 1 (sqrt.f64 (.f64 2 (/.f64 a (fma.f64 y x (.f64 (*.f64 t z) -9)))))))
	37.7b	(/.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)))))
✓	7.4b	(/.f64 1 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 (*.f64 t z) -9))))
	7.5b	(/.f64 1 (.f64 a (/.f64 2 (fma.f64 y x (.f64 (*.f64 t z) -9)))))
	32.2b	(.f64 (.f64 y x) (/.f64 1/2 a))
	32.3b	(/.f64 1 (.f64 2 (/.f64 a (.f64 y x))))
	36.5b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (sqrt.f64 (/.f64 1/2 a))) (sqrt.f64 (/.f64 1/2 a)))
✓	7.5b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
	8.1b	(.f64 (/.f64 (fma.f64 y x (.f64 (.f64 t z) -9)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/2 (cbrt.f64 a)))
	33.1b	(.f64 (.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
	37.9b	(/.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))))))
	33.1b	(/.f64 1 (.f64 -2/9 (/.f64 a (.f64 t z))))
	8.1b	(.f64 (.f64 (fma.f64 -9 (.f64 z t) (.f64 x y)) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))

Compiler

Compiled 4931 to 2952 computations (40.1% saved)

regimes1.1s (18.1%)

Accuracy

Total 0.4b remaining (5.3%)

Threshold costs 0.4b (5.3%)

Counts

89 → 1

Compiler

Compiled 23524 to 16497 computations (29.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	17
1	21	17
2	20	17

end211.0ms (3.5%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 430 to 302 computations (29.8% saved)

Details

analyze1.5s (24.8%)

sample1.7s (29.1%)

simplify206.0ms (3.4%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series49.0ms (0.8%)

rewrite8.0ms (0.1%)

simplify100.0ms (1.7%)

prune101.0ms (1.7%)

localize9.0ms (0.1%)

series55.0ms (0.9%)

rewrite15.0ms (0.2%)

simplify91.0ms (1.5%)

prune107.0ms (1.8%)

localize8.0ms (0.1%)

series53.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify118.0ms (2%)

prune79.0ms (1.3%)

localize9.0ms (0.2%)

series122.0ms (2%)

rewrite14.0ms (0.2%)

simplify115.0ms (1.9%)

prune183.0ms (3.1%)

regimes1.1s (18.1%)

simplify2.0ms (0%)

end211.0ms (3.5%)

Profiling