Details

analyze2.7s (30.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.5%	0.5%	0
0%	99.5%	0.5%	1
0%	99.5%	0.5%	2
0%	99.5%	0.5%	3
0%	99.5%	0.5%	4
0%	99.5%	0.5%	5
0%	99.5%	0.5%	6
0%	99.5%	0.5%	7
0%	99.5%	0.5%	8
0%	99.5%	0.5%	9
0%	99.5%	0.5%	10
0%	99.5%	0.5%	11
0%	99.5%	0.5%	12
0%	99.5%	0.5%	13
0%	99.5%	0.5%	14

Compiler

Compiled 42 to 30 computations (28.6% saved)

sample3.9s (44.3%)

Symmetry

(sort y z)

(sort b c)

(sort j k)

Results

2.2s	8256×	body	128	valid
1.7s	8224×	body	128	invalid

Compiler

Compiled 125 to 89 computations (28.8% saved)

simplify35.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

513×	`fma-neg_binary64`
388×	`sub-neg_binary64`
242×	`associate--r+_binary64`
237×	`distribute-rgt-neg-in_binary64`
213×	`associate--r-_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	43
1	77	37
2	278	35
3	986	35
4	2620	35
5	4613	35

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

3.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	7.1b	(fma.f64 t (fma.f64 (.f64 x 18) (.f64 y z) (.f64 a -4)) (fma.f64 b c (fma.f64 x (.f64 i -4) (.f64 j (.f64 k -27)))))

Status

Error

Program

▶

6.1b

(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))

7.1b

(fma.f64 t (fma.f64 (*.f64 x 18) (*.f64 y z) (*.f64 a -4)) (fma.f64 b c (fma.f64 x (*.f64 i -4) (*.f64 j (*.f64 k -27)))))

Compiler

Compiled 218 to 149 computations (31.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 a 4) t)
✓	0.4b	(.f64 (.f64 j 27) k)
✓	5.3b	(.f64 (.f64 (*.f64 x 18) y) z)
✓	5.8b	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)

series37.0ms (0.4%)

Counts

4 → 132

Calls

4 calls:

18.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)
9.0ms	(.f64 (.f64 (*.f64 x 18) y) z)
5.0ms	(.f64 (.f64 j 27) k)
4.0ms	(.f64 (.f64 a 4) t)

rewrite59.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

343×	`log1p-udef_binary64`
198×	`associate-r_binary64`
190×	`add-sqr-sqrt_binary64`
177×	`add-log-exp_binary64`
177×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	387	37
2	4607	37

Stop Event

1×	node limit

Counts

4 → 60

Calls

4 calls:

58.0ms	(.f64 (.f64 a 4) t)
58.0ms	(.f64 (.f64 j 27) k)
58.0ms	(.f64 (.f64 (*.f64 x 18) y) z)
58.0ms	(.f64 (.f64 (.f64 (.f64 x 18) y) z) t)

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

144×	`associate-l_binary64`
83×	`associate-r_binary64`
52×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	1320
1	44	1320
2	113	1320
3	246	1320
4	349	1320
5	349	1320

Stop Event

1×

saturated

Counts

192 → 66

prune112.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	8	68

Error

0.3b

Counts

68 → 8

Alt Table

Status	Error	Program
	7.6b	(-.f64 (-.f64 (+.f64 (-.f64 (pow.f64 (.f64 (.f64 x 18) (.f64 y (.f64 z t))) 1) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.9b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 4 (.f64 a t))) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 27 (*.f64 k j)))
	4.9b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 18 (.f64 y (.f64 z x))) t) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	3.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 t (.f64 z x)) (.f64 18 y)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
▶	3.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	7.1b	(fma.f64 t (fma.f64 (.f64 x 18) (.f64 y z) (.f64 a -4)) (fma.f64 b c (fma.f64 x (.f64 i -4) (.f64 j (.f64 k -27)))))
	15.6b	(-.f64 (-.f64 (+.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 x 18) (.f64 y (.f64 z t))) 3)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))

Compiler

Compiled 2902 to 1829 computations (37% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
	0.4b	(.f64 (.f64 j 27) k)
✓	3.7b	(.f64 t (.f64 z x))
✓	6.4b	(.f64 y (.f64 t (*.f64 z x)))

series48.0ms (0.5%)

Counts

3 → 0

Calls

3 calls:

24.0ms	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
16.0ms	(.f64 y (.f64 t (*.f64 z x)))
7.0ms	(.f64 t (.f64 z x))

rewrite43.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`log-prod_binary64`
306×	`pow-unpow_binary64`
265×	`pow2_binary64`
190×	`pow1/3_binary64`
184×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	203	30
2	2497	30

Stop Event

1×	node limit

Counts

3 → 59

Calls

3 calls:

42.0ms	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
42.0ms	(.f64 t (.f64 z x))
42.0ms	(.f64 y (.f64 t (*.f64 z x)))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

59 → 59

prune181.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Error

0.0b

Counts

83 → 8

Alt Table

Status	Error	Program
	15.6b	(-.f64 (-.f64 (+.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 x 18) (.f64 y (.f64 z t))) 3)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (+.f64 0 (.f64 (.f64 t z) (.f64 x y)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	7.6b	(-.f64 (-.f64 (+.f64 (-.f64 (pow.f64 (.f64 (.f64 x 18) (.f64 y (.f64 z t))) 1) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	3.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (pow.f64 (cbrt.f64 (.f64 t (.f64 z x))) 3))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	5.9b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x 18) y) z) t) (.f64 4 (.f64 a t))) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	3.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 t (.f64 z x)) (.f64 18 y)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	7.1b	(fma.f64 t (fma.f64 (.f64 x 18) (.f64 y z) (.f64 a -4)) (fma.f64 b c (fma.f64 x (.f64 i -4) (.f64 j (.f64 k -27)))))
▶	3.4b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 27 (*.f64 k j)))

Compiler

Compiled 3313 to 1910 computations (42.3% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 a 4) t)
	0.2b	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
	3.7b	(.f64 t (.f64 z x))
	6.4b	(.f64 y (.f64 t (*.f64 z x)))

prune148.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	77	7	84

Error

0.0b

Counts

84 → 7

Alt Table

Status	Error	Program
	3.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (pow.f64 (cbrt.f64 (.f64 t (.f64 z x))) 3))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (pow.f64 (.f64 (.f64 t z) (.f64 x y)) 1)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 27 (*.f64 k j)))
	7.6b	(-.f64 (-.f64 (+.f64 (-.f64 (pow.f64 (.f64 (.f64 x 18) (.f64 y (.f64 z t))) 1) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.2b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (pow.f64 (cbrt.f64 (.f64 (.f64 t z) (.f64 x y))) 3)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 27 (*.f64 k j)))
	3.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 t (.f64 z x)) (.f64 18 y)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	7.1b	(fma.f64 t (fma.f64 (.f64 x 18) (.f64 y z) (.f64 a -4)) (fma.f64 b c (fma.f64 x (.f64 i -4) (.f64 j (.f64 k -27)))))
▶	3.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 4 (.f64 a t))) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 27 (*.f64 k j)))

Compiler

Compiled 3262 to 1792 computations (45.1% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 27 (.f64 k j))
	0.2b	(.f64 18 (.f64 y (.f64 t (.f64 z x))))
	3.7b	(.f64 t (.f64 z x))
	6.4b	(.f64 y (.f64 t (*.f64 z x)))

series4.0ms (0%)

Counts

1 → 0

Calls

1 calls:

4.0ms

(*.f64 27 (*.f64 k j))

rewrite37.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
386×	`unpow-prod-down_binary64`
299×	`log-prod_binary64`
153×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1405	7

Stop Event

1×	node limit

Counts

1 → 17

Calls

1 calls:

37.0ms

(*.f64 27 (*.f64 k j))

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

17 → 17

prune136.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	76	7	83

Error

0.0b

Counts

83 → 7

Alt Table

Status	Error	Program
	3.8b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (pow.f64 (cbrt.f64 (.f64 t (.f64 z x))) 3))) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (pow.f64 (.f64 (.f64 t z) (.f64 x y)) 1)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 27 (*.f64 k j)))
	7.6b	(-.f64 (-.f64 (+.f64 (-.f64 (pow.f64 (.f64 (.f64 x 18) (.f64 y (.f64 z t))) 1) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	6.2b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (pow.f64 (cbrt.f64 (.f64 (.f64 t z) (.f64 x y))) 3)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 27 (*.f64 k j)))
	3.6b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 (.f64 t (.f64 z x)) (.f64 18 y)) (.f64 (.f64 a 4) t)) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 (*.f64 j 27) k))
	7.1b	(fma.f64 t (fma.f64 (.f64 x 18) (.f64 y z) (.f64 a -4)) (fma.f64 b c (fma.f64 x (.f64 i -4) (.f64 j (.f64 k -27)))))
✓	3.1b	(-.f64 (-.f64 (+.f64 (-.f64 (.f64 18 (.f64 y (.f64 t (.f64 z x)))) (.f64 4 (.f64 a t))) (.f64 b c)) (.f64 (.f64 x 4) i)) (.f64 27 (*.f64 k j)))

Compiler

Compiled 2993 to 1534 computations (48.7% saved)

regimes862.0ms (9.7%)

Accuracy

Total 1.6b remaining (95.9%)

Threshold costs 0b (0%)

Counts

28 → 3

Compiler

Compiled 21988 to 15840 computations (28% saved)

bsearch2.0ms (0%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

31×	`*-commutative_binary64`
22×	`+-commutative_binary64`
20×	`sub-neg_binary64`
16×	`distribute-rgt-neg-in_binary64`
14×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	222
1	91	222
2	143	222
3	177	222
4	199	222
5	209	222
6	211	222

Stop Event

1×

saturated

end403.0ms (4.5%)

Remove

(sort j k)

(sort b c)

Compiler

Compiled 1881 to 1138 computations (39.5% saved)

Details

analyze2.7s (30.2%)

sample3.9s (44.3%)

simplify35.0ms (0.4%)

prune5.0ms (0.1%)

localize20.0ms (0.2%)

series37.0ms (0.4%)

rewrite59.0ms (0.7%)

simplify44.0ms (0.5%)

prune112.0ms (1.3%)

localize19.0ms (0.2%)

series48.0ms (0.5%)

rewrite43.0ms (0.5%)

simplify7.0ms (0.1%)

prune181.0ms (2%)

localize23.0ms (0.3%)

prune148.0ms (1.7%)

localize22.0ms (0.3%)

series4.0ms (0%)

rewrite37.0ms (0.4%)

simplify9.0ms (0.1%)

prune136.0ms (1.5%)

regimes862.0ms (9.7%)

bsearch2.0ms (0%)

simplify10.0ms (0.1%)

end403.0ms (4.5%)

Profiling