Details

Time bar (total: 6.7s)

sample61.0ms

Algorithm
intervals
Results
39.0ms713×body80valid

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05114
115514
243014
3119514
4252614
5500114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.8b
(* (* b b) (+ 3.0 a))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
56.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
34.0ms
(* (* a a) (- 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (+ 3.0 a))

series280.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
50.0ms
(* (* a a) (- 1.0 a))
97.0ms
(pow (+ (* a a) (* b b)) 2.0)
30.0ms
(* (* b b) (+ 3.0 a))

simplify68.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0506651
12520583
25001583

prune269.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.4b
(* (pow a 2) (pow b 2))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
28×prod-exp
24×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
5×pow1 add-log-exp
4×cbrt-unprod
2×pow-prod-down *-commutative
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 87
Calls
3 calls:
13.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
28.0ms
(* 2 (* (pow a 2) (pow b 2)))
17.0ms
(* (pow a 2) (pow b 2))

series116.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
38.0ms
(* 2 (* (pow a 2) (pow b 2)))
30.0ms
(* (pow a 2) (pow b 2))

simplify49.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0297518
11270445
25001432

prune210.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.8b
(* (* b b) (+ 3.0 a))
29.6b
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod
4×cube-div associate-*r* add-log-exp
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ sqr-pow
2×cube-mult pow-to-exp cbrt-div pow-pow unpow3 associate-*r/ pow-exp
1×distribute-rgt-in distribute-lft-in pow1/3 associate-*l* *-commutative rem-cbrt-cube distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 89
Calls
4 calls:
75.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (+ 3.0 a))
62.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

series957.0ms

Counts
4 → 12
Calls
4 calls:
713.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
108.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (+ 3.0 a))
105.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

simplify75.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
05171412
126111294
250021288

prune280.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (+ 3.0 a))
15.1b
(sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))
15.1b
(sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))
29.6b
(cbrt (* (sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)) (sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))))

rewrite404.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
18×add-sqr-sqrt
16×cube-div sqrt-div
13×*-un-lft-identity
11×add-cube-cbrt
9×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
8×unpow-prod-down rem-sqrt-square cbrt-div cube-prod
4×frac-times associate-*r/ associate-*r* add-log-exp sqr-pow
3×pow-prod-down prod-exp cbrt-unprod
2×cube-mult sqrt-pow1 pow1/2 unpow3 associate-*l/
1×cbrt-prod distribute-rgt-in distribute-lft-in pow1/3 associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 95
Calls
4 calls:
31.0ms
(* (* b b) (+ 3.0 a))
116.0ms
(sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))
117.0ms
(sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))
137.0ms
(cbrt (* (sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)) (sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))))

series1.1s

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* b b) (+ 3.0 a))
492.0ms
(sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))
493.0ms
(sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))
103.0ms
(cbrt (* (sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)) (sqrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))))

simplify74.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04682235
122372007
250032006

prune416.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes198.0ms

Accuracy

97.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.3b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04855
14855

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20279×body80valid