Details

Time bar (total: 6.7s)

sample47.0ms

Algorithm
intervals
Results
30.0ms626×body80valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0268
1518
2887
31537
43577
515727
650027

prune12.0ms

Pruning

2 alts after pruning (2 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)))
0.0b
(+ (* a a) (* b b))
0.0b
(* 4.0 (* b b))
0.4b
(pow (+ (* a a) (* b b)) 2.0)

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×fma-def add-log-exp
6×unpow-prod-down
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×+-commutative flip3-+ sum-log flip-+ sqr-pow
1×pow-to-exp pow-pow associate-*r* pow-exp *-commutative unswap-sqr
Counts
4 → 74
Calls
4 calls:
60.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
7.0ms
(+ (* a a) (* b b))
16.0ms
(* 4.0 (* b b))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series204.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
24.0ms
(+ (* a a) (* b b))
26.0ms
(* 4.0 (* b b))
94.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0339438
11458396
25001385

prune348.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(pow (+ (* a a) (* b b)) 2.0)
11.2b
(sqrt (pow (+ (* a a) (* b b)) 2.0))
11.2b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×unpow-prod-down sqrt-prod
12×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log rem-sqrt-square pow-unpow sqr-pow
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-to-exp pow-pow sqrt-pow1 pow1/2 pow-exp
Counts
4 → 80
Calls
4 calls:
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
15.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
16.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series461.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(pow (+ (* a a) (* b b)) 2.0)
97.0ms
(pow (+ (* a a) (* b b)) 2.0)
134.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
134.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0138560
1470522
21671512
35002504

prune623.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
11.8b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
11.8b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
11.8b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
245.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
30.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
33.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
30.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series649.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
174.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
173.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
174.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify153.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 3 (130.0ms)

IterNodesCost
02721903
110001779
246031626
350011617

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
0.0b
(* 2 (pow a 2))
1.3b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×add-exp-log associate-*r*
7×add-cube-cbrt
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-+ distribute-lft-out
Counts
3 → 57
Calls
3 calls:
9.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
12.0ms
(* 2 (pow a 2))
0.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series145.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
24.0ms
(* 2 (pow a 2))
70.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify35.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0215372
1947344
25002343

prune274.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes178.0ms

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
01514
11514

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s20662×body80valid