Details

Time bar (total: 5.4s)

sample59.0ms

Algorithm
intervals
Results
39.0ms719×body80valid

simplify92.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
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 sqr-pow
Counts
4 → 79
Calls
4 calls:
25.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
15.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
55.0ms
(* (* a a) (+ 1.0 a))
108.0ms
(pow (+ (* a a) (* b b)) 2.0)
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify69.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0504702
12520622
25002622

prune268.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.6b
(* (pow a 2) (pow b 2))

rewrite42.0ms

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×*-un-lft-identity add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt add-log-exp
5×pow1
4×cbrt-unprod
3×sum-log
2×pow-prod-down *-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ distribute-lft-out
Counts
3 → 90
Calls
3 calls:
19.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
10.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series131.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
36.0ms
(* 2 (* (pow a 2) (pow b 2)))
38.0ms
(* (pow a 2) (pow b 2))

simplify49.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0330587
11424506
25001495

prune214.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))
2.6b
(* (pow a 2) (pow b 2))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
18×unswap-sqr
16×add-cbrt-cube
15×associate-*r* prod-exp
14×pow1 unpow-prod-down
12×*-un-lft-identity
10×add-cube-cbrt associate-*l* unpow2 sqr-pow
7×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp add-log-exp
4×associate-*r/
3×distribute-rgt-in sub-neg distribute-lft-in *-commutative
2×flip3-- flip--
1×flip3-+ diff-log flip-+ distribute-lft-out
Counts
4 → 112
Calls
4 calls:
6.0ms
(- 1.0 (* 3.0 a))
15.0ms
(* (* a a) (+ 1.0 a))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
9.0ms
(* (pow a 2) (pow b 2))

series362.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(- 1.0 (* 3.0 a))
49.0ms
(* (* a a) (+ 1.0 a))
57.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
32.0ms
(* (pow a 2) (pow b 2))

simplify71.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0474593
12437482
25003478

prune334.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 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) (- 1.0 (* 3.0 a)))))) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.1b
(* (* b b) (- 1.0 (* 3.0 a)))
32.8b
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod
4×cube-div add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×distribute-rgt-in cube-mult pow-to-exp sub-neg cbrt-div pow-pow distribute-lft-in flip3-+ unpow3 associate-*r/ pow-exp flip-+
1×flip3-- pow1/3 associate-*l* *-commutative flip-- rem-cbrt-cube rem-cube-cbrt unswap-sqr
Counts
4 → 90
Calls
4 calls:
38.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
30.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
786.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3)
103.0ms
(pow (+ (* a a) (* b b)) 2.0)
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
110.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

simplify79.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
05281543
125771405
250011399

prune287.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes129.0ms

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
02715
12715

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20420×body80valid