Details

Time bar (total: 4.8s)

sample40.0ms

Algorithm
intervals
Results
22.0ms603×body80valid

simplify50.0ms

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

localize12.0ms

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

rewrite429.0ms

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:
346.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
8.0ms
(+ (* a a) (* b b))
63.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series275.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
33.0ms
(+ (* a a) (* b b))
64.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify55.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0398829
11760685
25001672

prune238.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 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))
0.0b
(* 2 (pow a 2))
0.5b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
24×add-sqr-sqrt
16×add-cube-cbrt
12×prod-diff
11×add-log-exp
9×add-exp-log
8×associate-*r*
6×add-cbrt-cube distribute-lft-out
4×pow1 expm1-log1p-u unpow-prod-down fma-neg log1p-expm1-u unswap-sqr
3×fma-def associate-*l* prod-exp
2×diff-log sum-log fma-udef distribute-lft-out-- unpow2 sqr-pow
1×+-commutative pow-to-exp sub-neg associate-+l+ flip3-- flip3-+ pow-exp associate--l+ *-commutative flip-- cbrt-unprod flip-+ difference-of-squares
Counts
4 → 92
Calls
4 calls:
77.0ms
(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
9.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
13.0ms
(* 2 (pow a 2))
0.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series204.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (+ (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))
25.0ms
(* 2 (pow a 2))
73.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify55.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0322886
11427748
25001748

prune278.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 2.0 (pow a 2))
0.0b
(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.5b
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
8×add-exp-log associate-*r*
7×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube add-log-exp
4×unpow-prod-down unswap-sqr
3×pow1 expm1-log1p-u fma-def associate-*l* prod-exp log1p-expm1-u
2×fma-udef unpow2 sqr-pow
1×+-commutative pow-to-exp associate-+l+ flip3-+ pow-exp sum-log *-commutative cbrt-unprod flip-+
Counts
3 → 56
Calls
3 calls:
12.0ms
(* 2.0 (pow a 2))
7.0ms
(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series168.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 2.0 (pow a 2))
68.0ms
(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
75.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify36.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0230391
11013352
25002345

prune189.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))
0.5b
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))
22.7b
(sqrt (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))))
22.7b
(sqrt (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ fma-udef
Counts
4 → 54
Calls
4 calls:
0.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))
0.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))
5.0ms
(sqrt (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))))
5.0ms
(sqrt (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))))

series809.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))
78.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))
332.0ms
(sqrt (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))))
322.0ms
(sqrt (+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b))))

simplify101.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0171658
1649640
22915640
35001638

prune255.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes78.0ms

Accuracy

98.4% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.0b

bsearch103.0ms

Steps
ItersRangePoint
9
1.6312015655505496e-11
0.024130789021135513
9.00135537302134e-08
8
-21.084339142203387
-0.0006592480666379122
-0.0006735223120487487

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03517
13517

end0.0ms

sample1.2s

Algorithm
intervals
Results
758.0ms20441×body80valid