Details

Time bar (total: 5.5s)

sample48.0ms

Algorithm
intervals
Results
31.0ms656×body80valid

simplify80.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05114
115514
243014
3119514
4252614
5500114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
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 distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
23.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
16.0ms
(* (* a a) (- 1.0 a))
13.0ms
(* (* b b) (+ 3.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series294.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
55.0ms
(* (* a a) (- 1.0 a))
32.0ms
(* (* b b) (+ 3.0 a))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify74.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0506651
12520583
25001583

prune247.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
9.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite157.0ms

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×frac-times add-cbrt-cube 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 → 87
Calls
4 calls:
114.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
14.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
13.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
14.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series760.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
181.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
184.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
186.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03433024
111932795
250012567

prune397.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 2 (* (pow a 2) (pow b 2)))
0.9b
(* (pow a 2) (pow b 2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log
28×prod-exp
23×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×associate-*l*
10×unpow2 sqr-pow
9×associate-*r* add-cbrt-cube
7×add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-unprod
2×pow-prod-down *-commutative add-log-exp
Counts
2 → 76
Calls
2 calls:
13.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series68.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(* 2 (* (pow a 2) (pow b 2)))
33.0ms
(* (pow a 2) (pow b 2))

simplify40.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0229393
1907329
25002318

prune153.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
0.3b
(* (* b b) (+ 3.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
33.0b
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod
4×cube-div associate-*r* add-log-exp
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ sqr-pow
2×cube-mult pow-to-exp cbrt-div pow-pow unpow3 associate-*r/ pow-exp
1×distribute-rgt-in distribute-lft-in pow1/3 associate-*l* *-commutative rem-cbrt-cube distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 89
Calls
4 calls:
35.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
13.0ms
(* (* b b) (+ 3.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
27.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

series1.0s

Counts
4 → 12
Calls
4 calls:
783.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3)
33.0ms
(* (* b b) (+ 3.0 a))
104.0ms
(pow (+ (* a a) (* b b)) 2.0)
110.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 3))

simplify91.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
05171412
126111294
250021288

prune270.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes150.0ms

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
02514
12514

end0.0ms

sample1.3s

Algorithm
intervals
Results
980.0ms20310×body80valid