Details

Time bar (total: 18.7s)

sample103.0ms

Algorithm
intervals
Results
68.0ms659×body80valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
15129
215429
345229
4142829
done500029

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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
(pow (+ (* a a) (* b b)) 2.0)
0.8b
(* (* b b) (+ 3.0 a))

rewrite143.0ms

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×pow-unpow unpow-prod-down
2×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
80.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
27.0ms
(* (* a a) (- 1.0 a))
8.0ms
(pow (+ (* a a) (* b b)) 2.0)
24.0ms
(* (* b b) (+ 3.0 a))

series397.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
77.0ms
(* (* a a) (- 1.0 a))
122.0ms
(pow (+ (* a a) (* b b)) 2.0)
50.0ms
(* (* b b) (+ 3.0 a))

simplify2.5s

Counts
93 → 93
Iterations

Useful iterations: 2 (822.0ms)

IterNodesCost
01791446
15581337
238031209
done50001209

prune530.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(* (* (* b b) (* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a)))) (cbrt (+ 3.0 a)))
0.6b
(* (* b b) (* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a))))

rewrite380.0ms

Algorithm
rewrite-expression-head
Rules
78×cbrt-div
58×pow1
44×associate-*r/
39×flip3-+ flip-+
37×add-exp-log
36×frac-times
32×*-un-lft-identity
29×pow-prod-down
28×cbrt-prod
24×add-sqr-sqrt
22×prod-exp cbrt-unprod
21×add-cbrt-cube
18×associate-*l/
16×add-cube-cbrt
15×associate-*r*
9×swap-sqr associate-*l*
7×distribute-lft-out
6×pow1/3 pow-prod-up
5×pow-plus unswap-sqr
4×pow-sqr add-log-exp
3×pow2 pow-unpow unpow-prod-down *-commutative
1×pow-to-exp pow-pow pow-exp sqr-pow
Counts
4 → 164
Calls
4 calls:
41.0ms
(* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a)))
8.0ms
(pow (+ (* a a) (* b b)) 2.0)
239.0ms
(* (* (* b b) (* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a)))) (cbrt (+ 3.0 a)))
84.0ms
(* (* b b) (* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a)))
151.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* (* b b) (* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a)))) (cbrt (+ 3.0 a)))
169.0ms
(* (* b b) (* (cbrt (+ 3.0 a)) (cbrt (+ 3.0 a))))

simplify2.8s

Counts
176 → 176
Iterations

Useful iterations: 2 (927.0ms)

IterNodesCost
02603577
17953327
247222900
done50012900

prune810.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (+ 3.0 a))
8.7b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×cbrt-prod add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
8×add-cube-cbrt
6×cbrt-div
4×flip3-+ associate-*r* flip-+ add-log-exp
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
2×associate-*r/
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 63
Calls
4 calls:
25.0ms
(* (* b b) (+ 3.0 a))
30.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
32.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
30.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* b b) (+ 3.0 a))
252.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
249.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
200.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify979.0ms

Counts
75 → 75
Iterations

Useful iterations: done (976.0ms)

IterNodesCost
01222535
13552399
220592166
done50002135

prune491.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

8.7b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.7b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×pow1 flip3-+ add-cbrt-cube pow1/3 add-exp-log flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
28.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
25.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
26.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
29.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
255.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
250.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
248.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
251.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify2.1s

Counts
64 → 64
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0803004
12012848
27152588
347742520
done50012516

prune704.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes247.0ms

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
02140
12940
done2940

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.1s20551×body80valid