Details

sample65.0ms

Algorithm

intervals

Results

46.0ms

626×

body

valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	55	15
1	179	14
2	561	13
3	1824	13
4	5002	13

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 3.0 a))
0.1b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log`
9×	`prod-diff` `add-cbrt-cube`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `unpow-prod-down` `pow-unpow` `fma-neg` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-*r/` `flip--`
1×	`pow-to-exp` `pow-pow` `diff-log` `associate-l` `pow-exp` `*-commutative` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

3.0ms	(- 1.0 (* 3.0 a))
1.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
9.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- 1.0 (* 3.0 a))
60.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
121.0ms	(pow (+ (* a a) (* b b)) 2.0)
60.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	370	604
1	1558	520
2	5002	506

prune289.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	5	95

Merged error: 0.1b

Counts

95 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cbrt (+ (* a a) (* b b))) 2.0)
8.4b	(cbrt (+ (* a a) (* b b)))
8.4b	(cbrt (+ (* a a) (* b b)))
8.4b	(cbrt (+ (* a a) (* b b)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cbrt-div`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

6.0ms	(pow (cbrt (+ (* a a) (* b b))) 2.0)
4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(pow (cbrt (+ (* a a) (* b b))) 2.0)
107.0ms	(cbrt (+ (* a a) (* b b)))
102.0ms	(cbrt (+ (* a a) (* b b)))
110.0ms	(cbrt (+ (* a a) (* b b)))

simplify107.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	224	589
1	806	555
2	3031	546
3	5002	541

prune629.0ms

Filtered

80 candidates to 69 candidates (86.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	77	8	85

Merged error: 0.0b

Counts

85 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (+ (* a a) (* b b)))
8.4b	(cbrt (+ (* a a) (* b b)))
8.4b	(cbrt (+ (* a a) (* b b)))
8.4b	(cbrt (+ (* a a) (* b b)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
7.0ms	(cbrt (+ (* a a) (* b b)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (+ (* a a) (* b b)))
107.0ms	(cbrt (+ (* a a) (* b b)))
104.0ms	(cbrt (+ (* a a) (* b b)))
101.0ms	(cbrt (+ (* a a) (* b b)))

simplify62.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	132	524
1	449	488
2	1529	476
3	5001	476

prune508.0ms

Filtered

72 candidates to 72 candidates (100.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	70	10	80

Merged error: 0.0b

Counts

80 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (+ (* a a) (* b b)))
8.4b	(cbrt (+ (* a a) (* b b)))
8.4b	(cbrt (+ (* a a) (* b b)))
8.4b	(cbrt (+ (* a a) (* b b)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (+ (* a a) (* b b)))
109.0ms	(cbrt (+ (* a a) (* b b)))
111.0ms	(cbrt (+ (* a a) (* b b)))
102.0ms	(cbrt (+ (* a a) (* b b)))

simplify62.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	132	524
1	449	488
2	1529	476
3	5001	476

prune438.0ms

Filtered

72 candidates to 72 candidates (100.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	72	10	82

Merged error: 0.0b

Counts

82 → 10

regimes199.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.4s

20286×

body

valid