Details

Time bar (total: 5.9s)

sample53.0ms

Algorithm
intervals
Results
32.0ms666×body80valid

simplify73.0ms

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

localize20.0ms

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)
1.2b
(* (* b b) (+ 3.0 a))

rewrite126.0ms

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:
53.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
32.0ms
(* (* a a) (- 1.0 a))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
29.0ms
(* (* b b) (+ 3.0 a))

series310.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
57.0ms
(* (* a a) (- 1.0 a))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)
33.0ms
(* (* b b) (+ 3.0 a))

simplify68.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0506651
12520583
25001583

prune251.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

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 (+ 3.0 a))))))
0.1b
(* (* a a) (- 1.0 a))
0.2b
(* b (* b (+ 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
11×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt
7×distribute-rgt-in distribute-lft-in
6×associate-*r/ associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
4×associate-*l*
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ *-commutative flip-+
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 81
Calls
4 calls:
52.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))
30.0ms
(* (* a a) (- 1.0 a))
28.0ms
(* b (* b (+ 3.0 a)))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series304.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))
50.0ms
(* (* a a) (- 1.0 a))
38.0ms
(* b (* b (+ 3.0 a)))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify63.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0497650
12357582
25003582

prune257.0ms

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)
0.3b
(* (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))) (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))))
8.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))
8.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×sqrt-prod
22×pow1
16×add-cube-cbrt *-un-lft-identity sqrt-div
10×sqrt-pow1 pow1/2
8×flip3-+ swap-sqr flip-+
7×add-exp-log
6×associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×frac-times add-log-exp unswap-sqr
3×unpow-prod-down pow-unpow pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 pow-to-exp pow-pow pow-plus sqrt-unprod pow-exp prod-exp rem-square-sqrt *-commutative cbrt-unprod sqr-pow
Counts
4 → 104
Calls
4 calls:
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
239.0ms
(* (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))) (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))))
56.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))
58.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(pow (+ (* a a) (* b b)) 2.0)
122.0ms
(* (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))) (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a))))))))
173.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))
178.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))

simplify68.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
03602295
115712071
250012005

prune350.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(pow (sqrt (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))) 3)
8.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))
8.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
17×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
10×pow1
9×cube-prod
8×sqrt-div
6×add-exp-log pow-unpow pow-pow sqrt-pow1
5×add-cbrt-cube
4×pow1/2 add-log-exp
3×flip3-+ flip-+
2×cube-div pow-to-exp rem-sqrt-square pow-exp sqr-pow
1×cube-mult unpow3 sqrt-pow2 rem-cube-cbrt
Counts
4 → 89
Calls
4 calls:
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
61.0ms
(pow (sqrt (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))) 3)
56.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))
59.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))

series633.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(pow (+ (* a a) (* b b)) 2.0)
175.0ms
(pow (sqrt (sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))) 3)
177.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))
173.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* b (* b (+ 3.0 a)))))))

simplify62.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04671786
117851694
250011654

prune387.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03333
13333

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s20539×body80valid