Details

Time bar (total: 5.1s)

sample39.0ms

Algorithm
intervals
Results
24.0ms654×body80valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
0268
1518
2887
31537
43577
515727
650027

prune5.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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:
4.0ms
(+ (* a a) (* b b))
7.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series237.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* a a) (* b b))
74.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
26.0ms
(* 4.0 (* b b))
109.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify42.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0339438
11458396
25002385

prune415.0ms

Filtered
86 candidates to 66 candidates (76.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite35.0ms

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:
15.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
192.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
194.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
189.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify143.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 3 (126.0ms)

IterNodesCost
02721903
110001779
246031626
350011617

prune379.0ms

Filtered
107 candidates to 86 candidates (80.4%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 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))
0.0b
(* 2 (pow a 2))
2.4b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite12.0ms

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:
4.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
6.0ms
(* 2 (pow a 2))
1.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series169.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
34.0ms
(* 2 (pow a 2))
81.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify34.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0215372
1947344
25002343

prune190.0ms

Filtered
66 candidates to 46 candidates (69.7%)
Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
32.3b
(cbrt (+ (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)) (- (* (* 4.0 (* b b)) (* 4.0 (* b b))) (* (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))))
33.5b
(cbrt (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
10×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt cbrt-div
4×pow1 add-exp-log expm1-log1p-u flip3-+ pow1/3 add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
1×sum-cubes distribute-lft-out
Counts
4 → 62
Calls
4 calls:
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
17.0ms
(cbrt (+ (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)) (- (* (* 4.0 (* b b)) (* 4.0 (* b b))) (* (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))))
13.0ms
(cbrt (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
189.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
194.0ms
(cbrt (+ (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)) (- (* (* 4.0 (* b b)) (* 4.0 (* b b))) (* (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))))
170.0ms
(cbrt (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)))

simplify59.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03301471
112141363
250011326

prune442.0ms

Filtered
74 candidates to 71 candidates (95.9%)
Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes143.0ms

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
0158
1158

end0.0ms

sample1.1s

Algorithm
intervals
Results
750.0ms20313×body80valid