Details

Time bar (total: 5.6s)

sample97.0ms

Algorithm
intervals
Results
78.0ms742×body80valid

simplify70.0ms

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (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)
0.4b
(* (* b b) (+ 3.0 a))

rewrite59.0ms

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:
23.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
14.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
15.0ms
(* (* b b) (+ 3.0 a))

series287.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
49.0ms
(* (* a a) (- 1.0 a))
99.0ms
(pow (+ (* a a) (* b b)) 2.0)
35.0ms
(* (* b b) (+ 3.0 a))

simplify69.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0506651
12520583
25001583

prune249.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (+ 3.0 a))
0.4b
(* (* b b) (+ 3.0 a))
9.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
2×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 78
Calls
4 calls:
14.0ms
(* (* b b) (+ 3.0 a))
15.0ms
(* (* b b) (+ 3.0 a))
27.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
27.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* b b) (+ 3.0 a))
32.0ms
(* (* b b) (+ 3.0 a))
166.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
166.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0321932
11454858
25002856

prune304.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.5b
(* (pow a 2) (pow b 2))

rewrite48.0ms

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:
18.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
12.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series172.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
50.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
38.0ms
(* 2 (* (pow a 2) (pow b 2)))
32.0ms
(* (pow a 2) (pow b 2))

simplify57.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0375699
11613622
25001616

prune256.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

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))
0.4b
(* (* b b) (+ 3.0 a))
2.5b
(* (pow a 2) (pow b 2))

rewrite79.0ms

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:
38.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
14.0ms
(* (* a a) (- 1.0 a))
14.0ms
(* (* b b) (+ 3.0 a))
9.0ms
(* (pow a 2) (pow b 2))

series176.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
50.0ms
(* (* a a) (- 1.0 a))
35.0ms
(* (* b b) (+ 3.0 a))
31.0ms
(* (pow a 2) (pow b 2))

simplify118.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
0704838
13965716
25002712

prune390.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes119.0ms

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
02730
12730

end0.0ms

sample2.4s

Algorithm
intervals
Results
2.1s20373×body80valid