Details

analyze1.5s (23%)

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)

sample1.5s (24.2%)

Symmetry

(sort x y)

(sort z t)

Results

1.0s	8256×	body	128	valid
419.0ms	3265×	body	128	invalid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify208.0ms (3.3%)

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

5.9b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 100 to 69 computations (31% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
✓	0.2b	(.f64 (.f64 z 9) t)
✓	5.6b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

series52.0ms (0.8%)

Counts

3 → 132

Calls

3 calls:

37.0ms	(/.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)

rewrite96.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

282×	`expm1-udef_binary64`
282×	`log1p-udef_binary64`
155×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`

Counts

3 → 107

Calls

3 calls:

94.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
94.0ms	(.f64 (.f64 z 9) t)
94.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	309	35
2	4170	35
3	4932	35

simplify170.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1901×	`fma-def_binary64`
641×	`fma-neg_binary64`
512×	`cancel-sign-sub-inv_binary64`
426×	`associate-/l*_binary64`
420×	`distribute-rgt-neg-in_binary64`

Counts

239 → 121

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	1734
1	88	1566
2	213	1566
3	545	1566
4	1159	1566
5	2165	1566
6	2856	1566
7	3415	1566
8	3409	1566
9	3498	1566
10	3534	1566
11	5162	1566

prune125.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	109	12	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	111	12	123

Error

5.6b

Counts

123 → 12

Alt Table

Status	Error	Program
	35.9b	(cbrt.f64 (pow.f64 (.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a)) 3))
	6.8b	(.f64 (cbrt.f64 (.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (/.f64 1/2 a))) (pow.f64 (cbrt.f64 (.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))) 2))
	6.1b	(pow.f64 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9)))) -1)
	6.0b	(.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))
	33.2b	(pow.f64 (sqrt.f64 (.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))) 2)
	34.3b	(/.f64 (.f64 y x) (.f64 a 2))
	36.0b	(.f64 (sqrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) (.f64 (sqrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) (/.f64 1/2 a)))
	30.9b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
	36.0b	(/.f64 (pow.f64 (sqrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) 2) (*.f64 a 2))
	30.9b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	6.9b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) 2) a) (/.f64 (cbrt.f64 (fma.f64 x y (.f64 t (*.f64 z -9)))) 2))
▶	6.0b	(/.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (*.f64 a 2))

Compiler

Compiled 2941 to 1869 computations (36.5% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (.f64 t (.f64 z -9)))
✓	0.2b	(.f64 t (.f64 z -9))
✓	5.6b	(/.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (*.f64 a 2))

series51.0ms (0.8%)

Counts

3 → 132

Calls

3 calls:

36.0ms	(/.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (*.f64 a 2))
11.0ms	(fma.f64 x y (.f64 t (.f64 z -9)))
4.0ms	(.f64 t (.f64 z -9))

rewrite67.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`prod-diff_binary64`
243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
214×	`log-pow_binary64`
135×	`add-sqr-sqrt_binary64`

Counts

3 → 84

Calls

3 calls:

64.0ms	(fma.f64 x y (.f64 t (.f64 z -9)))
64.0ms	(.f64 t (.f64 z -9))
64.0ms	(/.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (*.f64 a 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	268	35
2	3249	35
3	4912	35

simplify160.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1901×	`fma-def_binary64`
641×	`fma-neg_binary64`
512×	`cancel-sign-sub-inv_binary64`
426×	`associate-/l*_binary64`
420×	`distribute-rgt-neg-in_binary64`

Counts

216 → 96

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	1734
1	88	1566
2	213	1566
3	545	1566
4	1159	1566
5	2165	1566
6	2856	1566
7	3415	1566
8	3409	1566
9	3498	1566
10	3534	1566
11	5162	1566

prune74.0ms (1.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	96	12	108

Error

5.6b

Counts

108 → 12

Alt Table

Status	Error	Program
	35.9b	(cbrt.f64 (pow.f64 (.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a)) 3))
	6.8b	(.f64 (cbrt.f64 (.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (/.f64 1/2 a))) (pow.f64 (cbrt.f64 (.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))) 2))
	6.1b	(pow.f64 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9)))) -1)
▶	6.0b	(.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))
	33.2b	(pow.f64 (sqrt.f64 (.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))) 2)
	34.3b	(/.f64 (.f64 y x) (.f64 a 2))
	36.0b	(.f64 (sqrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) (.f64 (sqrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) (/.f64 1/2 a)))
	30.9b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
	36.0b	(/.f64 (pow.f64 (sqrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) 2) (*.f64 a 2))
	30.9b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	6.9b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) 2) a) (/.f64 (cbrt.f64 (fma.f64 x y (.f64 t (*.f64 z -9)))) 2))
✓	6.0b	(/.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (*.f64 a 2))

Compiler

Compiled 2094 to 1365 computations (34.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (.f64 t (.f64 z -9)))
	0.2b	(.f64 t (.f64 z -9))
✓	5.7b	(.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))

series42.0ms (0.7%)

Counts

1 → 60

Calls

1 calls:

42.0ms

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

rewrite59.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`log-prod_binary64`
242×	`expm1-udef_binary64`
242×	`log1p-udef_binary64`
231×	`prod-diff_binary64`
213×	`log-pow_binary64`

Counts

1 → 32

Calls

1 calls:

58.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	269	17
2	3136	17
3	5709	17

simplify132.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1880×	`fma-def_binary64`
637×	`fma-neg_binary64`
506×	`cancel-sign-sub-inv_binary64`
421×	`distribute-rgt-neg-in_binary64`
414×	`associate-/l*_binary64`

Counts

92 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	1032
1	85	936
2	209	936
3	535	936
4	1152	936
5	2159	936
6	2838	936
7	3335	936
8	3381	936
9	3468	936
10	3505	936
11	5102	936

prune82.0ms (1.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	88	11	99

Error

5.6b

Counts

99 → 11

Alt Table

Status	Error	Program
	35.9b	(cbrt.f64 (pow.f64 (.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a)) 3))
	6.8b	(.f64 (cbrt.f64 (.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (/.f64 1/2 a))) (pow.f64 (cbrt.f64 (.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))) 2))
▶	6.1b	(pow.f64 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9)))) -1)
✓	6.0b	(.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))
	30.9b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
	28.1b	(/.f64 (/.f64 (.f64 (fma.f64 x y (.f64 t (.f64 z -9))) 1/2) (cbrt.f64 (.f64 a a))) (cbrt.f64 a))
✓	6.0b	(/.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (*.f64 a 2))
	34.3b	(.f64 (.f64 y x) (/.f64 1/2 a))
	36.0b	(.f64 (pow.f64 (sqrt.f64 (fma.f64 x y (.f64 t (*.f64 z -9)))) 2) (/.f64 1/2 a))
	30.9b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	6.9b	(.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) 2) (cbrt.f64 (fma.f64 x y (.f64 t (.f64 z -9))))) (/.f64 1/2 a))

Compiler

Compiled 1779 to 1149 computations (35.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x y (.f64 t (.f64 z -9)))
	0.2b	(.f64 t (.f64 z -9))
✓	0.3b	(pow.f64 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9)))) -1)
✓	5.6b	(/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9))))

series451.0ms (7.1%)

Counts

2 → 120

Calls

2 calls:

379.0ms	(pow.f64 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9)))) -1)
72.0ms	(/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9))))

rewrite123.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
240×	`prod-diff_binary64`
211×	`fma-neg_binary64`
205×	`fma-udef_binary64`

Counts

2 → 95

Calls

2 calls:

121.0ms	(pow.f64 (/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9)))) -1)
121.0ms	(/.f64 (.f64 a 2) (fma.f64 x y (.f64 t (*.f64 z -9))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	309	34
2	3595	34
3	4929	34
4	4949	34
5	4949	34

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

571×	`associate-*r/_binary64`
541×	`associate-*l/_binary64`
405×	`fma-def_binary64`
305×	`associate-/r/_binary64`
223×	`times-frac_binary64`

Counts

215 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	4036
1	469	3932
2	1755	3564
3	5014	3564

prune145.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	174	10	184

Error

5.6b

Counts

184 → 10

Alt Table

Status	Error	Program
✓	6.0b	(.f64 (fma.f64 x y (.f64 t (*.f64 z -9))) (/.f64 1/2 a))
	6.1b	(/.f64 (/.f64 1 (.f64 a 2)) (/.f64 1 (fma.f64 x y (.f64 t (*.f64 z -9)))))
	30.9b	(/.f64 (.f64 -9 (.f64 t z)) (*.f64 a 2))
	28.1b	(/.f64 (/.f64 (.f64 (fma.f64 x y (.f64 t (.f64 z -9))) 1/2) (cbrt.f64 (.f64 a a))) (cbrt.f64 a))
✓	6.0b	(/.f64 (fma.f64 x y (.f64 t (.f64 z -9))) (*.f64 a 2))
	34.3b	(.f64 (.f64 y x) (/.f64 1/2 a))
	6.1b	(pow.f64 (.f64 2 (/.f64 a (fma.f64 (.f64 t z) -9 (*.f64 y x)))) -1)
	36.0b	(.f64 (pow.f64 (sqrt.f64 (fma.f64 x y (.f64 t (*.f64 z -9)))) 2) (/.f64 1/2 a))
	30.9b	(.f64 -9/2 (/.f64 (.f64 t z) a))
	6.9b	(.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 x y (.f64 t (.f64 z -9)))) 2) (cbrt.f64 (fma.f64 x y (.f64 t (.f64 z -9))))) (/.f64 1/2 a))

Compiler

Compiled 3973 to 2548 computations (35.9% saved)

regimes903.0ms (14.2%)

Accuracy

Total 0.5b remaining (6.4%)

Threshold costs 0.5b (6.4%)

Counts

71 → 1

Compiler

Compiled 17351 to 12722 computations (26.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	33
1	35	33
2	41	33
3	44	33
4	45	33
5	44	33

end291.0ms (4.6%)

Remove: (sort x y)
Compiler: Compiled 409 to 287 computations (29.8% saved)

Details

analyze1.5s (23%)

sample1.5s (24.2%)

simplify208.0ms (3.3%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series52.0ms (0.8%)

rewrite96.0ms (1.5%)

simplify170.0ms (2.7%)

prune125.0ms (2%)

localize13.0ms (0.2%)

series51.0ms (0.8%)

rewrite67.0ms (1.1%)

simplify160.0ms (2.5%)

prune74.0ms (1.2%)

localize8.0ms (0.1%)

series42.0ms (0.7%)

rewrite59.0ms (0.9%)

simplify132.0ms (2.1%)

prune82.0ms (1.3%)

localize10.0ms (0.2%)

series451.0ms (7.1%)

rewrite123.0ms (1.9%)

simplify87.0ms (1.4%)

prune145.0ms (2.3%)

regimes903.0ms (14.2%)

simplify5.0ms (0.1%)

end291.0ms (4.6%)

Profiling