Details

Time bar (total: 5.6s)

sample50.0ms

Algorithm
intervals
Results
34.0ms624×body80valid

simplify80.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05314
117313
253212
3168112
4427812
5500112

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.2b
(* (* b b) (+ 3.0 a))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt *-un-lft-identity prod-diff
32×add-cube-cbrt
24×distribute-rgt-in distribute-lft-in
22×associate-+l+
15×pow1 add-exp-log
14×add-cbrt-cube
12×associate-*r/
9×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u sub-neg flip3-+ frac-add flip-+ log1p-expm1-u
3×unpow-prod-down pow-unpow flip3-- flip--
2×associate-+r+ associate-*l* *-commutative unswap-sqr
1×+-commutative pow-to-exp pow-pow fma-def pow-exp sum-log distribute-lft-out distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 134
Calls
4 calls:
14.0ms
(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
18.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

series238.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
55.0ms
(* (* a a) (- 1.0 a))
99.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify110.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
07301165
14038906
25001903

prune410.0ms

Filtered
146 candidates to 98 candidates (67.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
1.2b
(* (* b b) (+ 3.0 a))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
30×*-un-lft-identity
26×add-exp-log add-cube-cbrt
18×unpow-prod-down prod-diff
16×associate-*r* add-cbrt-cube
15×prod-exp
14×pow1
13×distribute-rgt-in distribute-lft-in
11×unswap-sqr
10×sqr-pow
9×associate-*l*
7×swap-sqr pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×*-commutative
2×sub-neg associate-+r+ flip3-+ flip-+
1×+-commutative pow2 flip3-- fma-def sum-log pow-sqr pow-prod-up flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 143
Calls
4 calls:
5.0ms
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
16.0ms
(* (* a a) (- 1.0 a))
11.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
14.0ms
(* (* b b) (+ 3.0 a))

series338.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(+ (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2))) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
53.0ms
(* (* a a) (- 1.0 a))
150.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (fma a a (* b b)) (/ 2.0 2)))
31.0ms
(* (* b b) (+ 3.0 a))

simplify101.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07231510
138861232
250021210

prune391.0ms

Filtered
155 candidates to 88 candidates (56.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
0.2b
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
1.2b
(* (* b b) (+ 3.0 a))
10.9b
(sqrt (fma a a (* b b)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
80×add-exp-log
69×prod-exp
34×pow-to-exp pow-exp
27×add-sqr-sqrt
21×associate-*r*
18×unpow-prod-down
16×add-cbrt-cube
15×*-un-lft-identity
13×add-cube-cbrt
10×pow1 unswap-sqr
9×associate-*l* sqr-pow
7×cbrt-unprod
6×sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down *-commutative
2×associate-*r/
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 flip3-+ pow1/2 flip-+ fma-udef hypot-def distribute-lft-out
Counts
4 → 138
Calls
4 calls:
16.0ms
(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
9.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
14.0ms
(* (* b b) (+ 3.0 a))
1.0ms
(sqrt (fma a a (* b b)))

series625.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(* (* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4)))) (pow (sqrt (fma a a (* b b))) (/ 2.0 2)))
309.0ms
(* (pow (fma a a (* b b)) (/ 2.0 2)) (pow (hypot a b) (* 2 (/ 2.0 4))))
31.0ms
(* (* b b) (+ 3.0 a))
41.0ms
(sqrt (fma a a (* b b)))

simplify82.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07051747
128281583
250011445

prune566.0ms

Filtered
150 candidates to 88 candidates (58.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* b b) (+ 3.0 a))
11.5b
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
11.5b
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
11.5b
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
13×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod sqr-pow
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ associate-*l* *-commutative flip-+ distribute-lft-out unswap-sqr
Counts
4 → 77
Calls
4 calls:
14.0ms
(* (* b b) (+ 3.0 a))
1.0ms
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
1.0ms
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
1.0ms
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* b b) (+ 3.0 a))
149.0ms
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
153.0ms
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))
153.0ms
(cbrt (pow (fma a a (* b b)) (/ 2.0 2)))

simplify40.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0272636
11132582
25002576

prune382.0ms

Filtered
89 candidates to 72 candidates (80.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03228
13228

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s20551×body80valid