Details

Time bar (total: 5.3s)

sample52.0ms

Algorithm
intervals
Results
34.0ms652×body80valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
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 unpow-prod-down pow-unpow fma-neg
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 → 98
Calls
4 calls:
3.0ms
(- 1.0 (* 3.0 a))
8.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
11.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- 1.0 (* 3.0 a))
51.0ms
(* (* a a) (+ 1.0 a))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0464609
12250529
25002522

prune307.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
13×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
10×distribute-rgt-in distribute-lft-in
7×fma-def
6×unpow-prod-down associate-*r/ prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ *-commutative flip-+ sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- unswap-sqr
Counts
4 → 100
Calls
4 calls:
8.0ms
(+ (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)
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* a (* a (+ 1.0 a)))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0555829
12608723
25002713

prune363.0ms

Pruning

6 alts after pruning (6 fresh and 0 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)))))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity prod-diff
10×distribute-rgt-in distribute-lft-in
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg sqrt-div associate-*r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 100
Calls
4 calls:
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms
(* (* 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)))))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
168.0ms
(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)))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03871304
116361186
250021176

prune396.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

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)))))))
9.6b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.6b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×add-exp-log add-cbrt-cube
6×cbrt-prod prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×flip3-+ associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod flip-+
2×sub-neg pow1/3 sqrt-div associate-*r/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 80
Calls
4 calls:
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
10.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

series586.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
170.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
181.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))
188.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04791534
119061409
250021392

prune462.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes129.0ms

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
03132
13132

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20466×body80valid