Details

Time bar (total: 4.9s)

sample51.0ms

Algorithm
intervals
Results
34.0ms652×body80valid

simplify101.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×associate-*r/
3×distribute-rgt-in sub-neg unpow-prod-down pow-unpow distribute-lft-in
2×flip3-- associate-*l* *-commutative flip-- unswap-sqr
1×pow-to-exp pow-pow flip3-+ diff-log pow-exp flip-+ distribute-lft-out sqr-pow
Counts
4 → 78
Calls
4 calls:
3.0ms
(- 1.0 (* 3.0 a))
7.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- 1.0 (* 3.0 a))
48.0ms
(* (* a a) (+ 1.0 a))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
72.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0408475
11999415
25002415

prune240.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×distribute-rgt-in distribute-lft-in
6×associate-*r/ pow-prod-down prod-exp cbrt-unprod add-log-exp
4×associate-*r* associate-*l*
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ *-commutative flip-+
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- unswap-sqr sqr-pow
Counts
4 → 79
Calls
4 calls:
7.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a))))))
7.0ms
(* a (* a (+ 1.0 a)))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a))))))
46.0ms
(* a (* a (+ 1.0 a)))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify59.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0495703
12301619
25003619

prune245.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
8.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

series637.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
236.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
178.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
175.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify46.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03321080
11388980
25001978

prune305.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
8.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-sqr-sqrt
9×add-exp-log sqrt-prod add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
169.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
169.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
166.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03321266
113881182
250011179

prune311.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes84.0ms

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
02915
12915

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20466×body80valid