Details

Time bar (total: 5.6s)

sample61.0ms

Algorithm
intervals
Results
39.0ms673×body80valid

simplify93.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05315
116115
245915
3132315
4299215
5500115

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.5b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out sqr-pow
Counts
4 → 79
Calls
4 calls:
52.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
29.0ms
(* (* a a) (+ 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms
(* (* a a) (+ 1.0 a))
96.0ms
(pow (+ (* a a) (* b b)) 2.0)
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify66.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0504702
12520622
25002622

prune250.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* b b) (- 1.0 (* 3.0 a)))
20.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
28.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series643.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
134.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
323.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
138.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0266651
11020585
25001579

prune304.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

4.7b
(exp (log (cbrt (pow (+ (* a a) (* b b)) 2.0))))
20.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
10×log-prod exp-sum
5×pow1 exp-prod
4×add-exp-log pow1/3 add-cbrt-cube add-log-exp sqr-pow
2×log-pow
1×rem-exp-log
Counts
4 → 68
Calls
4 calls:
14.0ms
(exp (log (cbrt (pow (+ (* a a) (* b b)) 2.0))))
8.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series568.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(exp (log (cbrt (pow (+ (* a a) (* b b)) 2.0))))
147.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
138.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
141.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify151.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
0149693
1294649
2894621
33850603
45002603

prune352.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
1.4b
(* (pow a 2) (pow b 2))

rewrite291.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
17×add-log-exp
16×unswap-sqr
15×add-exp-log
14×unpow-prod-down *-un-lft-identity
10×unpow2 sqr-pow
9×prod-exp
8×associate-*r* associate-*l*
7×add-cube-cbrt
6×pow-to-exp pow-exp sum-log
5×add-cbrt-cube
3×pow1 diff-log
2×distribute-lft-out distribute-lft-out--
1×+-commutative sub-neg associate-+r+ flip3-- flip3-+ pow-prod-down associate--l+ *-commutative flip-- cbrt-unprod flip-+ difference-of-squares
Counts
3 → 83
Calls
3 calls:
236.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
35.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
17.0ms
(* (pow a 2) (pow b 2))

series128.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
46.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
30.0ms
(* (pow a 2) (pow b 2))

simplify49.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0334682
11417617
25001605

prune205.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes158.0ms

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
02715
12715

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20628×body80valid