Details

Time bar (total: 5.8s)

sample44.0ms

Algorithm
intervals
Results
25.0ms666×body80valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0258
1418
2678
31198
43098
514948
650018

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* b b))
0.0b
(+ (* a a) (* b b))
0.0b
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite315.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube
7×add-cube-cbrt
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×diff-log sum-log
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ associate-*r* pow-exp associate--l+ *-commutative flip-- flip-+ distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 63
Calls
4 calls:
15.0ms
(* 4.0 (* b b))
8.0ms
(+ (* a a) (* b b))
280.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series228.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* 4.0 (* b b))
27.0ms
(+ (* a a) (* b b))
74.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
100.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify36.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0338488
11360446
25001439

prune154.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×unpow-prod-down pow-unpow
7×pow1 add-exp-log
5×cbrt-prod
4×add-cbrt-cube add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
2×cbrt-div
1×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
116.0ms
(cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(pow (+ (* a a) (* b b)) 2.0)

series484.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
104.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify106.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0216633
1740599
22851597
35001595

prune260.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b
(- (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))) 1.0)
0.0b
(* 2.0 (* (pow a 2) (pow b 2)))
2.9b
(* (pow a 2) (pow b 2))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
27×add-sqr-sqrt
18×add-log-exp
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1 sum-log
4×cbrt-unprod
3×diff-log
2×pow-prod-down *-commutative
1×+-commutative sub-neg associate-+l+ flip3-- flip3-+ associate--l+ flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
49.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
237.0ms
(- (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))) 1.0)
25.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
16.0ms
(* (pow a 2) (pow b 2))

series197.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
66.0ms
(- (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))) 1.0)
35.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
32.0ms
(* (pow a 2) (pow b 2))

simplify54.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0402875
11770759
25001747

prune231.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
0.1b
(pow (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
15.9b
(cbrt (pow (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0) 3))

rewrite784.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
16×cbrt-prod
13×unpow-prod-down
12×add-cube-cbrt
10×cube-prod
9×add-log-exp
6×pow1 add-exp-log pow-unpow
5×add-cbrt-cube distribute-lft-out-- difference-of-squares
4×cube-div
3×flip3-- flip-- sqr-pow
2×cube-mult pow-to-exp cbrt-div pow-pow diff-log unpow3 pow-exp
1×sub-neg pow1/3 associate--l+ sum-log rem-cbrt-cube rem-cube-cbrt
Counts
4 → 89
Calls
4 calls:
272.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
274.0ms
(pow (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0) 3)
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
225.0ms
(cbrt (pow (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0) 3))

series723.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
463.0ms
(pow (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0) 3)
106.0ms
(pow (+ (* a a) (* b b)) 2.0)
77.0ms
(cbrt (pow (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0) 3))

simplify51.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03591219
114941164
250021158

prune219.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes144.0ms

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
0158
1158

end0.0ms

sample1.2s

Algorithm
intervals
Results
734.0ms20539×body80valid