Details

Time bar (total: 7.5s)

sample122.0ms

Algorithm
intervals
Results
103.0ms657×body80valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

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
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 72
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
60.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
114.0ms
(pow (+ (* a a) (* b b)) 2.0)
57.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0391706
11680606
25001592

prune299.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a a) (* b b))
0.0b
(fma 1.0 (fma a a (* b b)) (pow a 3))
0.0b
(fma 4.0 (fma 1.0 (fma a a (* b b)) (pow a 3)) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×unpow-prod-down pow-unpow
2×fma-udef
1×+-commutative pow-to-exp pow-pow fma-def flip3-+ pow-exp sum-log flip-+ sqr-pow
Counts
4 → 53
Calls
4 calls:
3.0ms
(+ (* a a) (* b b))
0.0ms
(fma 1.0 (fma a a (* b b)) (pow a 3))
0.0ms
(fma 4.0 (fma 1.0 (fma a a (* b b)) (pow a 3)) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series289.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* a a) (* b b))
42.0ms
(fma 1.0 (fma a a (* b b)) (pow a 3))
104.0ms
(fma 4.0 (fma 1.0 (fma a a (* b b)) (pow a 3)) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
115.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify144.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 3 (132.0ms)

IterNodesCost
0261436
11145382
24619375
35001374

prune262.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log
19×add-cbrt-cube
18×add-sqr-sqrt prod-diff
15×distribute-rgt-in add-cube-cbrt *-un-lft-identity distribute-lft-in
9×associate-*r* pow-prod-down prod-exp cbrt-unprod
6×sub-neg associate-*r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow flip3-- associate-*l* *-commutative flip-- unswap-sqr
1×pow-to-exp pow-pow pow-exp sqr-pow
Counts
4 → 118
Calls
4 calls:
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
16.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(pow (+ (* a a) (* b b)) 2.0)
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify47.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0304905
11350773
25002753

prune523.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
6.9b
(cbrt (+ (* a a) (* b b)))
6.9b
(cbrt (+ (* a a) (* b b)))
6.9b
(cbrt (+ (* a a) (* b b)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×cbrt-div prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 78
Calls
4 calls:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms
(cbrt (+ (* a a) (* b b)))
2.0ms
(cbrt (+ (* a a) (* b b)))
2.0ms
(cbrt (+ (* a a) (* b b)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
112.0ms
(cbrt (+ (* a a) (* b b)))
112.0ms
(cbrt (+ (* a a) (* b b)))
110.0ms
(cbrt (+ (* a a) (* b b)))

simplify49.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0331646
11480584
25001567

prune562.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes331.0ms

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
02113
12113

end0.0ms

sample3.5s

Algorithm
intervals
Results
3.1s20396×body80valid