Details

Time bar (total: 5.3s)

sample53.0ms

Algorithm
intervals
Results
35.0ms613×body80valid

simplify94.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite57.0ms

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:
26.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
11.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* a a) (+ 1.0 a))
100.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify67.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0504702
12520622
25002622

prune252.0ms

Filtered
91 candidates to 61 candidates (67.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.3b
(* (pow a 2) (pow b 2))

rewrite31.0ms

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×add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
5×pow1 add-log-exp
4×cbrt-unprod
2×pow-prod-down *-commutative
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 87
Calls
3 calls:
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
13.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series120.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
35.0ms
(* 2 (* (pow a 2) (pow b 2)))
31.0ms
(* (pow a 2) (pow b 2))

simplify46.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0297518
11270445
25001432

prune200.0ms

Filtered
96 candidates to 47 candidates (49.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b
(* (* a a) (+ 1.0 a))
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))
3.3b
(* (pow a 2) (pow b 2))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
28×add-exp-log
19×unswap-sqr
18×associate-*r/ associate-*r* add-cbrt-cube
16×pow1 prod-exp
14×unpow-prod-down *-un-lft-identity
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
Counts
4 → 126
Calls
4 calls:
36.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
17.0ms
(* (* a a) (+ 1.0 a))
11.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
9.0ms
(* (pow a 2) (pow b 2))

series196.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
52.0ms
(* (* a a) (+ 1.0 a))
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
31.0ms
(* (pow a 2) (pow b 2))

simplify127.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
0724912
14116774
25002770

prune404.0ms

Filtered
138 candidates to 80 candidates (58.0%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize19.0ms

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)
1.3b
(* (* b b) (- 1.0 (* 3.0 a)))
30.8b
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

rewrite83.0ms

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:
34.0ms
(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)
15.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
28.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

series1.0s

Counts
4 → 12
Calls
4 calls:
767.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3)
102.0ms
(pow (+ (* a a) (* b b)) 2.0)
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
107.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

simplify77.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05281543
125771405
250011399

prune272.0ms

Filtered
102 candidates to 59 candidates (57.8%)
Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes334.0ms

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

sample1.4s

Algorithm
intervals
Results
1.0s20162×body80valid