Details

Time bar (total: 7.8s)

sample115.0ms

Algorithm
intervals
Results
97.0ms657×body80valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

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)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite62.0ms

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:
30.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
48.0ms
(* (* a a) (+ 1.0 a))
112.0ms
(pow (+ (* a a) (* b b)) 2.0)
48.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify79.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0564828
12826724
25001715

prune349.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (+ 1.0 a))
0.1b
(cbrt (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
10×pow1 add-exp-log
9×add-cbrt-cube
8×cbrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg flip3-+ pow1/3 associate-*r/ flip-+ distribute-lft-out
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 84
Calls
4 calls:
2.0ms
(cbrt (+ 1.0 a))
2.0ms
(cbrt (+ 1.0 a))
8.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (+ 1.0 a))
88.0ms
(cbrt (+ 1.0 a))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify58.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0460639
11868573
25002557

prune380.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
6.3b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.3b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite90.0ms

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:
15.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
30.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
30.0ms
(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:
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
360.0ms
(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)))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
03881304
116741186
250021176

prune380.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
6.3b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.9b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.9b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite75.0ms

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:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
30.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
16.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
15.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series611.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
185.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
182.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
192.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04801534
119441409
250011392

prune435.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes224.0ms

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
03122
13122

end0.0ms

sample3.3s

Algorithm
intervals
Results
3.0s20396×body80valid