Details

Time bar (total: 5.5s)

sample57.0ms

Algorithm
intervals
Results
34.0ms623×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

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))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.6b
(* (* b b) (+ 3.0 a))

rewrite135.0ms

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:
57.0ms
(+ (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))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (+ 3.0 a))

series324.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
51.0ms
(* (* a a) (- 1.0 a))
109.0ms
(pow (+ (* a a) (* b b)) 2.0)
37.0ms
(* (* b b) (+ 3.0 a))

simplify70.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0506651
12520583
25001583

prune256.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (+ 3.0 a))
9.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.0b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt
6×cbrt-div
4×flip3-+ associate-*r* flip-+ add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 63
Calls
4 calls:
32.0ms
(* (* b b) (+ 3.0 a))
30.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
32.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
31.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series817.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* b b) (+ 3.0 a))
192.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
192.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
400.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03381282
114701156
250021120

prune329.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.5b
(* (pow a 2) (pow b 2))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
14.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
35.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
27.0ms
(* 2 (* (pow a 2) (pow b 2)))
18.0ms
(* (pow a 2) (pow b 2))

series186.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
57.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
39.0ms
(* 2 (* (pow a 2) (pow b 2)))
37.0ms
(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0375699
11613622
25001616

prune254.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b
(* (* a a) (- 1.0 a))
0.6b
(* (* b b) (+ 3.0 a))
3.5b
(* (pow a 2) (pow b 2))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×add-exp-log
20×associate-*r*
19×unswap-sqr
18×associate-*r/ add-cbrt-cube
16×pow1 *-un-lft-identity prod-exp
14×unpow-prod-down
13×associate-*l*
12×add-cube-cbrt
10×unpow2 sqr-pow
8×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
4×distribute-rgt-in distribute-lft-in flip3-+ frac-add *-commutative flip-+ add-log-exp
3×flip3-- flip--
2×sub-neg
1×distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 128
Calls
4 calls:
85.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
33.0ms
(* (* a a) (- 1.0 a))
31.0ms
(* (* b b) (+ 3.0 a))
21.0ms
(* (pow a 2) (pow b 2))

series186.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
51.0ms
(* (* a a) (- 1.0 a))
37.0ms
(* (* b b) (+ 3.0 a))
33.0ms
(* (pow a 2) (pow b 2))

simplify108.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
0704874
13982716
25001712

prune392.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes138.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02945
12945

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20611×body80valid