Details

Time bar (total: 17.6s)

sample104.0ms

Algorithm
intervals
Results
73.0ms709×body80valid

simplify5.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216031
345131
4122331
5246931
6461831
done500131

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

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

rewrite178.0ms

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:
97.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
31.0ms
(* (* a a) (+ 1.0 a))
35.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series401.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
55.0ms
(* (* a a) (+ 1.0 a))
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
158.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify1.3s

Counts
91 → 91
Iterations

Useful iterations: 2 (446.0ms)

IterNodesCost
01751540
14801431
218341287
done50001287

prune373.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

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)))
1.8b
(* (pow a 2) (pow b 2))

rewrite92.0ms

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:
22.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
47.0ms
(* 2 (* (pow a 2) (pow b 2)))
20.0ms
(* (pow a 2) (pow b 2))

series141.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
47.0ms
(* 2 (* (pow a 2) (pow b 2)))
35.0ms
(* (pow a 2) (pow b 2))

simplify1.3s

Counts
96 → 96
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01221229
12961062
2927884
done5001874

prune582.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

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) (- 1.0 (* 3.0 a)))))) 3)
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
32.5b
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod
4×cube-div add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×distribute-rgt-in cube-mult pow-to-exp sub-neg cbrt-div pow-pow distribute-lft-in flip3-+ unpow3 associate-*r/ pow-exp flip-+
1×flip3-- pow1/3 associate-*l* *-commutative flip-- rem-cbrt-cube rem-cube-cbrt unswap-sqr
Counts
4 → 90
Calls
4 calls:
108.0ms
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3)
38.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
12.0ms
(pow (+ (* a a) (* b b)) 2.0)
95.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.2s
(pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3)
71.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
152.0ms
(pow (+ (* a a) (* b b)) 2.0)
153.0ms
(cbrt (pow (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 3))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: 2 (486.0ms)

IterNodesCost
01983426
15163088
218332694
done50012694

prune451.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes154.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
12731
done2731

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.3s20340×body80valid