Details

Time bar (total: 4.4s)

sample41.0ms

Algorithm
intervals
Results
25.0ms690×body80valid

simplify54.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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:
3.0ms
(+ (* a a) (* b b))
9.0ms
(* 4.0 (* b b))
26.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series227.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* a a) (* b b))
30.0ms
(* 4.0 (* b b))
63.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
106.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0339438
11458396
25001385

prune226.0ms

Pruning

4 alts after pruning (3 fresh and 1 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))
1.9b
(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))
0.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series152.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
24.0ms
(* 2 (pow a 2))
74.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify36.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0215372
1947344
25002343

prune200.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (* 4.0 (* b b)))
0.2b
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
26.5b
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
42×unpow-prod-down
40×cbrt-prod
23×fma-def
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×cube-prod
10×sqr-pow
7×add-exp-log
6×pow-unpow add-log-exp
5×pow1 pow-exp add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×cube-mult pow-to-exp unpow3
2×pow-pow
1×+-commutative flip3-+ pow1/3 sum-log rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 121
Calls
4 calls:
66.0ms
(+ (cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (* 4.0 (* b b)))
8.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
8.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series447.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ (cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (* 4.0 (* b b)))
121.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
112.0ms
(pow (+ (* a a) (* b b)) 2.0)
145.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify58.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0381888
11656821
25001771

prune353.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (pow (hypot a b) (/ 2.0 2)) 6)
0.0b
(pow (pow (hypot a b) (/ 2.0 2)) 6)
0.1b
(* (pow (pow (hypot a b) (/ 2.0 2)) 6) (pow (pow (hypot a b) (/ 2.0 2)) 6))
26.5b
(cbrt (* (pow (pow (hypot a b) (/ 2.0 2)) 6) (pow (pow (hypot a b) (/ 2.0 2)) 6)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
100×unpow-prod-down
52×add-sqr-sqrt
48×pow-exp
38×add-exp-log
32×sqr-pow
25×prod-exp unswap-sqr
24×pow-to-exp
22×add-cube-cbrt *-un-lft-identity
11×swap-sqr associate-*r* associate-*l*
6×pow-unpow add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-pow
1×cbrt-prod pow2 pow1/3 pow-prod-down pow-sqr *-commutative pow-prod-up cbrt-unprod
Counts
4 → 159
Calls
4 calls:
6.0ms
(pow (pow (hypot a b) (/ 2.0 2)) 6)
2.0ms
(pow (pow (hypot a b) (/ 2.0 2)) 6)
20.0ms
(* (pow (pow (hypot a b) (/ 2.0 2)) 6) (pow (pow (hypot a b) (/ 2.0 2)) 6))
6.0ms
(cbrt (* (pow (pow (hypot a b) (/ 2.0 2)) 6) (pow (pow (hypot a b) (/ 2.0 2)) 6)))

series644.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(pow (pow (hypot a b) (/ 2.0 2)) 6)
153.0ms
(pow (pow (hypot a b) (/ 2.0 2)) 6)
172.0ms
(* (pow (pow (hypot a b) (/ 2.0 2)) 6) (pow (pow (hypot a b) (/ 2.0 2)) 6))
168.0ms
(cbrt (* (pow (pow (hypot a b) (/ 2.0 2)) 6) (pow (pow (hypot a b) (/ 2.0 2)) 6)))

simplify57.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03821642
115451489
250011276

prune424.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes127.0ms

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
751.0ms20581×body80valid