Details

Time bar (total: 5.1s)

sample61.0ms

Algorithm
intervals
Results
44.0ms691×body80valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0258
1418
2678
31198
43098
514948
650018

prune2.0ms

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)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×+-commutative flip3-+ sum-log flip-+
1×pow-to-exp pow-pow associate-*r* pow-exp *-commutative unswap-sqr sqr-pow
Counts
4 → 58
Calls
4 calls:
3.0ms
(+ (* a a) (* b b))
6.0ms
(* 4.0 (* b b))
24.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series225.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* a a) (* b b))
24.0ms
(* 4.0 (* b b))
68.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify39.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0322413
11353379
25001379

prune164.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
73×cbrt-prod
46×add-sqr-sqrt
29×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
16×unswap-sqr
15×sqr-pow
11×pow1
10×swap-sqr associate-*r* associate-*l*
9×pow1/3
6×add-exp-log
4×add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
39.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series601.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
152.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
147.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
155.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify103.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
02111498
16811419
232741337
350011330

prune364.0ms

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
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.3b
(* (pow a 2) (pow b 2))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
28×prod-exp
24×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×add-cbrt-cube unpow2 sqr-pow
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
5×pow1 add-log-exp
4×cbrt-unprod
2×pow-prod-down *-commutative
1×+-commutative flip3-+ sum-log flip-+
Counts
3 → 87
Calls
3 calls:
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
14.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series122.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
41.0ms
(* 2 (* (pow a 2) (pow b 2)))
32.0ms
(* (pow a 2) (pow b 2))

simplify44.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0297518
11270445
25001432

prune196.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (* 4.0 4.0)) (pow b 4))
0.3b
(pow (+ (* a a) (* b b)) (* 2 2.0))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
35.3b
(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
13×add-exp-log
10×unpow-prod-down
9×times-frac
8×add-cbrt-cube
7×associate-*r*
6×pow1 associate-*l*
4×pow-unpow add-log-exp sqr-pow
3×pow-to-exp pow-exp prod-exp associate-/r* associate-/l* unswap-sqr
2×pow-pow associate-/r/ associate-/l/
1×cbrt-undiv distribute-lft-neg-out distribute-lft-neg-in neg-mul-1 flip3-- distribute-rgt-neg-in frac-2neg flip3-+ div-exp clear-num *-commutative flip-- cbrt-unprod flip-+ div-inv
Counts
4 → 92
Calls
4 calls:
7.0ms
(* (- (* 4.0 4.0)) (pow b 4))
4.0ms
(pow (+ (* a a) (* b b)) (* 2 2.0))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
74.0ms
(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series606.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (- (* 4.0 4.0)) (pow b 4))
101.0ms
(pow (+ (* a a) (* b b)) (* 2 2.0))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)
364.0ms
(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify72.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
04761315
125051189
250011186

prune332.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes124.0ms

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

sample1.7s

Algorithm
intervals
Results
1.3s21017×body80valid