Details

Time bar (total: 5.6s)

sample71.0ms

Algorithm
intervals
Results
53.0ms691×body80valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune6.0ms

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
(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)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite18.0ms

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)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(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))
49.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0391706
11680606
25001592

prune266.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)))) (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
1.0b
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod fma-udef
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 63
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
0.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series287.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
49.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
72.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify45.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0333685
11455579
25001568

prune277.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
26.4b
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
29×unpow-prod-down
20×cbrt-prod add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
14×cube-prod
12×add-exp-log
10×pow1 add-cbrt-cube
7×sqr-pow
6×pow-unpow prod-diff
5×distribute-rgt-in distribute-lft-in pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp associate-*r* pow-prod-down prod-exp cbrt-unprod
2×cube-mult sub-neg pow-pow unpow3 associate-*r/
1×flip3-- pow1/3 associate-*l* *-commutative flip-- rem-cbrt-cube rem-cube-cbrt unswap-sqr
Counts
4 → 118
Calls
4 calls:
8.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series423.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
103.0ms
(pow (+ (* a a) (* b b)) 2.0)
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
148.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify58.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0484933
12071873
25001849

prune384.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
26.2b
(cbrt (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log
9×add-cbrt-cube
8×cbrt-prod
6×unpow-prod-down 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×sub-neg pow1/3 associate-*r/ sqr-pow
1×pow-to-exp flip3-- pow-pow associate-*l* pow-exp *-commutative flip-- unswap-sqr
Counts
4 → 80
Calls
4 calls:
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
13.0ms
(cbrt (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
152.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
145.0ms
(cbrt (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)))

simplify45.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0404713
11634629
25002609

prune371.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes127.0ms

Accuracy

96.9% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 11.3b

bsearch177.0ms

Steps
ItersRangePoint
8
0.0005333266348582408
21.937063956757843
0.4178382122737707
8
-53.660684837311074
-0.05495133652606057
-2.403938157532335

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04243
14243

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.6s21017×body80valid