Details

Time bar (total: 6.0s)

sample59.0ms

Algorithm
intervals
Results
39.0ms699×body80valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
17×pow1 add-exp-log
16×add-sqr-sqrt add-cbrt-cube
14×*-un-lft-identity
12×add-cube-cbrt
10×associate-*r*
7×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
6×prod-diff
5×associate-*l*
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×pow-to-exp pow-pow pow-exp distribute-lft-out sqr-pow
Counts
4 → 106
Calls
4 calls:
13.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
8.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)

series298.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
52.0ms
(* (* a a) (+ 1.0 a))
57.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
117.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify121.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
0725894
14089793
25001790

prune365.0ms

Filtered
118 candidates to 82 candidates (69.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1144118
Fresh000
Picked101
Done000
Total1154119

Merged error: 0.0b

Counts
119 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
0.3b
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×add-exp-log
20×*-un-lft-identity
18×add-cube-cbrt unpow-prod-down associate-*r/ add-cbrt-cube
17×associate-*r*
16×pow1 prod-exp
12×associate-*l* unswap-sqr
10×sqr-pow
8×pow-prod-down cbrt-unprod
7×distribute-rgt-in distribute-lft-in swap-sqr
6×pow-to-exp prod-diff pow-exp
4×expm1-log1p-u flip3-+ frac-add *-commutative flip-+ log1p-expm1-u add-log-exp
3×flip3-- flip--
2×sub-neg
1×pow2 pow-sqr pow-prod-up distribute-lft-out
Counts
4 → 141
Calls
4 calls:
15.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
8.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
58.0ms
(* (* a a) (+ 1.0 a))
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
174.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))

simplify142.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
07941336
144601176
250011175

prune478.0ms

Filtered
153 candidates to 96 candidates (62.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1503153
Fresh123
Picked011
Done000
Total1516157

Merged error: 0.0b

Counts
157 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3) (sqrt (pow (fma a a (* b b)) (/ 2.0 2))))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
10.0b
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
10.0b
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
89×sqrt-prod
84×add-sqr-sqrt
61×unpow-prod-down
41×unswap-sqr
30×sqr-pow
27×associate-*l*
26×cube-prod
21×add-cube-cbrt *-un-lft-identity
14×add-exp-log
13×associate-*r*
11×add-cbrt-cube
10×pow1
6×rem-sqrt-square prod-diff prod-exp
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×pow-prod-down
2×sub-neg sqrt-pow1 pow1/2 associate-*r/ *-commutative
1×cube-mult pow-to-exp flip3-- pow-plus unpow3 pow-exp pow-prod-up flip--
Counts
4 → 167
Calls
4 calls:
19.0ms
(* (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3) (sqrt (pow (fma a a (* b b)) (/ 2.0 2))))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
3.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

series585.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (pow (sqrt (pow (fma a a (* b b)) (/ 2.0 2))) 3) (sqrt (pow (fma a a (* b b)) (/ 2.0 2))))
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
180.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))
175.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

simplify97.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
04992084
123351907
250011870

prune613.0ms

Filtered
179 candidates to 107 candidates (59.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1772179
Fresh404
Picked011
Done101
Total1823185

Merged error: 0b

Counts
185 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
10.0b
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt associate-*r/
16×pow1 add-exp-log add-cbrt-cube
14×*-un-lft-identity
12×add-cube-cbrt
10×associate-*r*
7×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp sqrt-prod cbrt-unprod
6×prod-diff
5×associate-*l*
4×expm1-log1p-u unpow-prod-down flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-- *-commutative flip-- unswap-sqr
2×sub-neg sqr-pow
1×sqrt-pow1 pow1/2 distribute-lft-out
Counts
4 → 108
Calls
4 calls:
12.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
8.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
59.0ms
(* (* a a) (+ 1.0 a))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
183.0ms
(sqrt (pow (fma a a (* b b)) (/ 2.0 2)))

simplify121.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
0734922
13965824
25001819

prune463.0ms

Filtered
120 candidates to 85 candidates (70.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1200120
Fresh011
Picked011
Done011
Total1203123

Merged error: 0b

Counts
123 → 3

regimes69.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03117
13117

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s20696×body80valid