Details

Time bar (total: 5.7s)

sample58.0ms

Algorithm
intervals
Results
39.0ms676×body80valid

simplify51.0ms

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

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)
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite61.0ms

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))))))
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)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
239.0ms
(* (* a a) (+ 1.0 a))
106.0ms
(pow (+ (* a a) (* b b)) 2.0)
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify73.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0564828
12826724
25001715

prune342.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a)))))
0.0b
(fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
25×distribute-rgt-in distribute-lft-in
20×associate-+r+
18×prod-diff
15×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log
9×add-cbrt-cube
6×sub-neg add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×unpow-prod-down pow-unpow fma-def associate-*r* pow-prod-down prod-exp cbrt-unprod
2×associate-*r/ fma-udef
1×+-commutative pow-to-exp associate-+l+ flip3-- pow-pow flip3-+ associate-*l* pow-exp sum-log *-commutative flip-- flip-+ unswap-sqr sqr-pow
Counts
4 → 99
Calls
4 calls:
7.0ms
(+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a)))))
0.0ms
(fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
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:
92.0ms
(+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a)))))
71.0ms
(fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05351128
122751002
25002992

prune388.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
10.6b
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))
10.6b
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))
10.6b
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))

rewrite20.0ms

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:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))
2.0ms
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))
2.0ms
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))

series802.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
250.0ms
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))
245.0ms
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))
252.0ms
(cbrt (+ (fma (pow a 2) (* (+ 1.0 a) 4.0) (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (* (* b b) (- 1.0 (* 3.0 a))))))

simplify57.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04131699
116691559
250011528

prune450.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
10.8b
(cbrt (+ (* a a) (* b b)))
10.8b
(cbrt (+ (* a a) (* b b)))
10.8b
(cbrt (+ (* a a) (* b b)))

rewrite20.0ms

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:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms
(cbrt (+ (* a a) (* b b)))
2.0ms
(cbrt (+ (* a a) (* b b)))
2.0ms
(cbrt (+ (* a a) (* b b)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
96.0ms
(cbrt (+ (* a a) (* b b)))
96.0ms
(cbrt (+ (* a a) (* b b)))
95.0ms
(cbrt (+ (* a a) (* b b)))

simplify45.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0331646
11480584
25001567

prune410.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes100.0ms

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
02815
12815

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s20274×body80valid