Details

Time bar (total: 5.8s)

sample61.0ms

Algorithm
intervals
Results
41.0ms719×body80valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
29.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
17.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
51.0ms
(* (* a a) (+ 1.0 a))
123.0ms
(pow (+ (* a a) (* b b)) 2.0)
61.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify78.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
0564828
12826724
25001715

prune346.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
0.2b
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×prod-diff
7×associate-*r*
6×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×sub-neg fma-neg
2×flip3-- associate-*l* *-commutative flip-- unswap-sqr
1×flip3-+ diff-log flip-+ fma-udef distribute-lft-out
Counts
4 → 89
Calls
4 calls:
3.0ms
(- 1.0 (* 3.0 a))
15.0ms
(* (* a a) (+ 1.0 a))
0.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
17.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- 1.0 (* 3.0 a))
52.0ms
(* (* a a) (+ 1.0 a))
140.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify60.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0448762
12130640
25003629

prune323.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* b b) (- 1.0 (* 3.0 a)))
18.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 84
Calls
4 calls:
13.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series602.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
179.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
176.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
185.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0315769
11231692
25002681

prune386.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

9.0b
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
9.0b
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
18.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
34×cbrt-prod
18×unpow-prod-down
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×sqrt-prod
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
Counts
4 → 74
Calls
4 calls:
5.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
5.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series718.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
180.0ms
(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
175.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
182.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify148.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
0179814
1384760
21210750
34950740
45001740

prune454.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02821
12821

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20420×body80valid