Details

Time bar (total: 19.9s)

sample76.0ms

Algorithm
intervals
Results
48.0ms665×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216131
348631
4164531
done500131

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

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

rewrite196.0ms

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:
85.0ms
(+ (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))
12.0ms
(pow (+ (* a a) (* b b)) 2.0)
45.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
57.0ms
(* (* a a) (+ 1.0 a))
181.0ms
(pow (+ (* a a) (* b b)) 2.0)
79.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.3s

Counts
91 → 91
Iterations

Useful iterations: 2 (823.0ms)

IterNodesCost
01751540
15511441
238261287
done50001287

prune441.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
6.3b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.3b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-*l* *-commutative flip-- flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
42.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
35.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
94.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
109.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series701.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
68.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
249.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
297.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify1.4s

Counts
92 → 92
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01202304
13422090
219001900
done50021892

prune483.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* b b) (- 1.0 (* 3.0 a)))
6.9b
(cbrt (+ (* a a) (* b b)))
6.9b
(cbrt (+ (* a a) (* b b)))
6.9b
(cbrt (+ (* a a) (* b b)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 64
Calls
4 calls:
40.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms
(cbrt (+ (* a a) (* b b)))
5.0ms
(cbrt (+ (* a a) (* b b)))
10.0ms
(cbrt (+ (* a a) (* b b)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
136.0ms
(cbrt (+ (* a a) (* b b)))
152.0ms
(cbrt (+ (* a a) (* b b)))
136.0ms
(cbrt (+ (* a a) (* b b)))

simplify1.8s

Counts
76 → 76
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01021069
12991022
21955884
done5000875

prune542.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

4.0b
(exp (log (cbrt (+ (* a a) (* b b)))))
6.9b
(cbrt (+ (* a a) (* b b)))
6.9b
(cbrt (+ (* a a) (* b b)))
6.9b
(cbrt (+ (* a a) (* b b)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×cbrt-div
6×log-prod exp-sum
5×pow1 exp-prod
4×add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
2×log-div exp-diff log-pow
1×rem-exp-log
Counts
4 → 60
Calls
4 calls:
22.0ms
(exp (log (cbrt (+ (* a a) (* b b)))))
11.0ms
(cbrt (+ (* a a) (* b b)))
11.0ms
(cbrt (+ (* a a) (* b b)))
23.0ms
(cbrt (+ (* a a) (* b b)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(exp (log (cbrt (+ (* a a) (* b b)))))
151.0ms
(cbrt (+ (* a a) (* b b)))
161.0ms
(cbrt (+ (* a a) (* b b)))
141.0ms
(cbrt (+ (* a a) (* b b)))

simplify2.7s

Counts
72 → 72
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0881074
1179996
2596818
33270806
done5002788

prune472.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes201.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02163
12963
done2963

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.0s20473×body80valid