Details

Time bar (total: 5.1s)

sample60.0ms

Algorithm
intervals
Results
38.0ms661×body80valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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

rewrite141.0ms

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:
63.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
33.0ms
(* (* a a) (+ 1.0 a))
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
13.0ms
(pow (+ (* a a) (* b b)) 2.0)

series291.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
49.0ms
(* (* a a) (+ 1.0 a))
43.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
98.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify72.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0564828
12826724
25001715

prune346.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))
0.2b
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
16×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt associate-*r*
7×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
6×prod-diff
5×associate-*l*
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×fma-udef distribute-lft-out
Counts
4 → 97
Calls
4 calls:
85.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
33.0ms
(* (* a a) (+ 1.0 a))
0.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
43.0ms
(* (* a a) (+ 1.0 a))
106.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify100.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06661047
13763904
25001897

prune544.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (fma a a (* b b)) (* 2 (/ 2.0 2))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
0.3b
(pow (fma a a (* b b)) (* 2 (/ 2.0 2)))

rewrite89.0ms

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 flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 98
Calls
4 calls:
19.0ms
(+ (pow (fma a a (* b b)) (* 2 (/ 2.0 2))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
34.0ms
(* (* a a) (+ 1.0 a))
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms
(pow (fma a a (* b b)) (* 2 (/ 2.0 2)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(+ (pow (fma a a (* b b)) (* 2 (/ 2.0 2))) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
45.0ms
(* (* a a) (+ 1.0 a))
46.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
102.0ms
(pow (fma a a (* b b)) (* 2 (/ 2.0 2)))

simplify73.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0562859
12888757
25002751

prune330.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 2 (pow a 2))
0.1b
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.0b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×add-exp-log associate-*r*
6×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down unswap-sqr
3×pow1 expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
2×fma-udef unpow2 sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod
Counts
3 → 49
Calls
3 calls:
13.0ms
(* 2 (pow a 2))
0.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
0.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series137.0ms

Counts
3 → 9
Calls
3 calls:
21.0ms
(* 2 (pow a 2))
55.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
61.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify179.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 3 (174.0ms)

IterNodesCost
0175315
1770276
24508274
35001270

prune176.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes92.0ms

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
02821
12821

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20781×body80valid