Details

Time bar (total: 5.3s)

sample82.0ms

Algorithm
intervals
Results
66.0ms657×body80valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0268
1518
2887
31537
43577
515727
650027

prune5.0ms

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

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
15×add-cube-cbrt
13×add-log-exp
9×prod-diff
8×fma-def
6×unpow-prod-down
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-unpow fma-neg sum-log
2×+-commutative flip3-+ diff-log flip-+ sqr-pow
1×pow-to-exp sub-neg flip3-- pow-pow pow-exp associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 83
Calls
4 calls:
163.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
29.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
3.0ms
(+ (* a a) (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series279.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
69.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
27.0ms
(+ (* a a) (* b b))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify56.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0398829
11760685
25001672

prune256.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
10.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
10.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×add-exp-log unpow-prod-down pow-unpow sqrt-prod
4×expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+ sqr-pow
Counts
4 → 72
Calls
4 calls:
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
30.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series402.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(pow (+ (* a a) (* b b)) 2.0)
106.0ms
(pow (+ (* a a) (* b b)) 2.0)
93.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
95.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify109.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0213702
1811666
23265656
35001656

prune291.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
0.0b
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
1.0b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt prod-diff
10×add-log-exp
6×distribute-lft-out
4×fma-neg
3×pow1 add-exp-log expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×diff-log sum-log fma-udef distribute-lft-out--
1×+-commutative sub-neg associate-+l+ flip3-- flip3-+ associate--l+ flip-- flip-+ difference-of-squares
Counts
3 → 63
Calls
3 calls:
46.0ms
(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
5.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
0.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series181.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
54.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
71.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify43.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0225781
11025655
25001655

prune195.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a a) (* b b))
0.2b
(pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
33.7b
(cbrt (pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down
6×pow1 add-exp-log pow-unpow cube-prod add-log-exp
5×add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×sqr-pow
2×cube-mult pow-to-exp pow-pow unpow3 pow-exp
1×+-commutative fma-def flip3-+ pow1/3 sum-log rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 81
Calls
4 calls:
3.0ms
(+ (* a a) (* b b))
1.0ms
(pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3)
7.0ms
(pow (+ (* a a) (* b b)) 2.0)
1.0ms
(cbrt (pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3))

series299.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a a) (* b b))
103.0ms
(pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3)
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
63.0ms
(cbrt (pow (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 3))

simplify45.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0341742
11493680
25002664

prune239.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes89.0ms

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
01718
11718

end0.0ms

sample2.3s

Algorithm
intervals
Results
2.0s20396×body80valid