Details

Time bar (total: 5.1s)

sample69.0ms

Algorithm
intervals
Results
49.0ms679×body80valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1

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))
0.4b
(pow (+ (* a a) (* b b)) 2.0)
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
11.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* a a) (+ 1.0 a))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify77.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0564828
12826724
25001715

prune319.0ms

Filtered
112 candidates to 80 candidates (71.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1075112
Fresh000
Picked101
Done000
Total1085113

Merged error: 0.0b

Counts
113 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
8.4b
(sqrt (+ (* a a) (* b b)))
8.4b
(sqrt (+ (* a a) (* b b)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×pow1
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff sqrt-prod
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ hypot-def
1×flip3-- associate-*l* *-commutative flip-- fma-udef unswap-sqr
Counts
4 → 79
Calls
4 calls:
1.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(sqrt (+ (* a a) (* b b)))
4.0ms
(sqrt (+ (* a a) (* b b)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
35.0ms
(sqrt (+ (* a a) (* b b)))
39.0ms
(sqrt (+ (* a a) (* b b)))

simplify55.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0379738
11669640
25001616

prune302.0ms

Filtered
91 candidates to 70 candidates (76.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New89291
Fresh404
Picked011
Done000
Total93396

Merged error: 0b

Counts
96 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (hypot a b) (* 2 2.0))
0.0b
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp pow-unpow hypot-udef flip3-- pow-pow pow-exp sum-log sqrt-pow2 flip-- distribute-lft-out
Counts
4 → 99
Calls
4 calls:
3.0ms
(pow (hypot a b) (* 2 2.0))
6.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(pow (hypot a b) (* 2 2.0))
131.0ms
(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* a a) (+ 1.0 a))
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify80.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
0558780
12839681
25002672

prune290.0ms

Filtered
111 candidates to 77 candidates (69.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1110111
Fresh011
Picked011
Done011
Total1113114

Merged error: 0b

Counts
114 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.2b
(pow (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (hypot a b) (* 2 2.0))) 3)
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
35.8b
(cbrt (pow (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (hypot a b) (* 2 2.0))) 3))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
10×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×cube-mult sub-neg unpow3 associate-*r/ sqr-pow
1×pow-to-exp flip3-- pow-pow pow1/3 associate-*l* pow-exp *-commutative flip-- rem-cbrt-cube fma-udef rem-cube-cbrt unswap-sqr
Counts
4 → 91
Calls
4 calls:
1.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
2.0ms
(pow (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (hypot a b) (* 2 2.0))) 3)
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms
(cbrt (pow (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (hypot a b) (* 2 2.0))) 3))

series566.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
347.0ms
(pow (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (hypot a b) (* 2 2.0))) 3)
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
110.0ms
(cbrt (pow (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (hypot a b) (* 2 2.0))) 3))

simplify76.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04721297
121331162
250011151

prune301.0ms

Filtered
103 candidates to 63 candidates (61.2%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1030103
Fresh000
Picked011
Done022
Total1033106

Merged error: 0b

Counts
106 → 3

regimes60.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
12914

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s20618×body80valid