Details

Time bar (total: 7.1s)

sample96.0ms

Algorithm
intervals
Results
76.0ms639×body80valid

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune8.0ms

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
(+ (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)
1.3b
(* (* 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))))))
14.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
16.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
64.0ms
(* (* a a) (+ 1.0 a))
127.0ms
(pow (+ (* a a) (* b b)) 2.0)
63.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify85.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
0564828
12826724
25001715

prune385.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))
14.5b
(sqrt (pow (+ (* a a) (* b b)) 2.0))
14.5b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite35.0ms

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)
13.0ms
(* (* 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))

series551.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(pow (+ (* a a) (* b b)) 2.0)
65.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
173.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
184.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0343691
11458621
25002611

prune472.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* b b) (- 1.0 (* 3.0 a)))
9.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×cbrt-div prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 78
Calls
4 calls:
16.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
14.0ms
(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)))))))
15.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series730.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
225.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
224.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
223.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify72.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04011582
116891442
250021408

prune477.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 2 (pow a 2))
0.1b
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.8b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×add-exp-log associate-*r*
6×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down unswap-sqr
3×pow1 expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
2×fma-udef unpow2 sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod
Counts
3 → 49
Calls
3 calls:
7.0ms
(* 2 (pow a 2))
0.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
0.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series195.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* 2 (pow a 2))
77.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
88.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify207.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 3 (201.0ms)

IterNodesCost
0175315
1770276
24508274
35001270

prune201.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes154.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02721
12721

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.3s20597×body80valid