Details

Time bar (total: 7.5s)

sample118.0ms

Algorithm
intervals
Results
99.0ms650×body80valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 72
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
55.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify50.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0391706
11680606
25001592

prune477.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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)
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite59.0ms

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:
26.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(+ (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))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify76.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0564828
12826724
25001715

prune339.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
12.1b
(sqrt (pow (+ (* a a) (* b b)) 2.0))
12.1b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×sqrt-prod
13×add-cube-cbrt *-un-lft-identity
11×unpow-prod-down
10×pow1 add-exp-log
9×add-cbrt-cube
6×rem-sqrt-square prod-diff
5×distribute-rgt-in distribute-lft-in sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg sqrt-pow1 pow1/2 associate-*r/
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr
Counts
4 → 94
Calls
4 calls:
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series442.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
143.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
142.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0343691
11458621
25002611

prune421.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

12.1b
(sqrt (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (cbrt (pow (+ (* a a) (* b b)) 2.0))))
19.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.9b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
21×cbrt-prod
15×sqrt-pow1
12×pow1/3
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down pow-prod-up
6×pow-plus
5×pow-prod-down
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-sqr sqr-pow
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 77
Calls
4 calls:
47.0ms
(sqrt (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (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))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series589.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(sqrt (* (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))) (cbrt (pow (+ (* a a) (* b b)) 2.0))))
149.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
153.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
144.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify133.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (125.0ms)

IterNodesCost
0178739
1505686
22805667
35002661

prune391.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes147.0ms

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
02721
12721

end0.0ms

sample3.4s

Algorithm
intervals
Results
3.0s20311×body80valid