Details

Time bar (total: 12.0s)

sample58.0ms

Algorithm
intervals
Results
39.0ms717×body80valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01829
15129
213429
331729
469429
5148129
6320229
done500029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 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)
0.5b
(* (* b b) (+ 3.0 a))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity associate-*r/
9×associate-*r*
8×add-cube-cbrt
6×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod add-log-exp
4×sub-neg associate-+l+ flip3-+ frac-add flip-+
3×unpow-prod-down pow-unpow flip3-- flip--
2×associate-+r+ associate-*l* *-commutative unswap-sqr
1×+-commutative pow-to-exp pow-pow pow-exp sum-log distribute-lft-out distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 89
Calls
4 calls:
14.0ms
(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
14.0ms
(* (* a a) (- 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
14.0ms
(* (* b b) (+ 3.0 a))

series240.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))
56.0ms
(* (* a a) (- 1.0 a))
103.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

simplify1.4s

Counts
101 → 101
Iterations

Useful iterations: 2 (618.0ms)

IterNodesCost
01911484
15431351
223941247
done50001247

prune285.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* 1.0 (* a a)) (- (* b (* b (+ 3.0 a))) (pow a 3)))))
0.0b
(+ (* 1.0 (* a a)) (- (* b (* b (+ 3.0 a))) (pow a 3)))
0.1b
(* b (* b (+ 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log
9×distribute-rgt-in distribute-lft-in add-cbrt-cube
8×associate-+r+
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×associate-*r/ associate--l+
3×unpow-prod-down pow-unpow flip3-+ associate-*l* pow-prod-down prod-exp sum-log cbrt-unprod flip-+
2×+-commutative
1×pow-to-exp associate-+r- sub-neg pow-pow diff-log associate-*r* pow-exp *-commutative sqr-pow
Counts
4 → 73
Calls
4 calls:
25.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* 1.0 (* a a)) (- (* b (* b (+ 3.0 a))) (pow a 3)))))
43.0ms
(+ (* 1.0 (* a a)) (- (* b (* b (+ 3.0 a))) (pow a 3)))
12.0ms
(* b (* b (+ 3.0 a)))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series299.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* 1.0 (* a a)) (- (* b (* b (+ 3.0 a))) (pow a 3)))))
55.0ms
(+ (* 1.0 (* a a)) (- (* b (* b (+ 3.0 a))) (pow a 3)))
32.0ms
(* b (* b (+ 3.0 a)))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify753.0ms

Counts
85 → 85
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
01721640
14631541
216351399
done50001399

prune287.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (- (+ (* 1.0 (pow a 2)) (* 3.0 (pow b 2))) (pow a 3))))
0.0b
(- (+ (* 1.0 (pow a 2)) (* 3.0 (pow b 2))) (pow a 3))
0.1b
(* 3.0 (pow b 2))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
11×*-un-lft-identity add-log-exp
10×add-exp-log
9×add-cube-cbrt
8×unpow-prod-down associate-*r*
6×associate-+r+ add-cbrt-cube
5×pow1
4×difference-of-squares unswap-sqr sqr-pow
3×distribute-rgt-in sub-neg pow-unpow distribute-lft-in associate-*l* prod-exp associate--l+
2×pow-to-exp diff-log pow-exp sum-log unpow2
1×+-commutative flip3-- pow-pow flip3-+ cube-prod *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out--
Counts
4 → 80
Calls
4 calls:
34.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (- (+ (* 1.0 (pow a 2)) (* 3.0 (pow b 2))) (pow a 3))))
24.0ms
(- (+ (* 1.0 (pow a 2)) (* 3.0 (pow b 2))) (pow a 3))
6.0ms
(* 3.0 (pow b 2))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series263.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (- (+ (* 1.0 (pow a 2)) (* 3.0 (pow b 2))) (pow a 3))))
38.0ms
(- (+ (* 1.0 (pow a 2)) (* 3.0 (pow b 2))) (pow a 3))
23.0ms
(* 3.0 (pow b 2))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify1.8s

Counts
92 → 92
Iterations

Useful iterations: 3 (658.0ms)

IterNodesCost
01761697
14121600
212201483
348031407
done50001407

prune301.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 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)))
0.0b
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
2.0b
(* (pow a 2) (pow b 2))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
27×add-sqr-sqrt
16×unswap-sqr
15×add-log-exp
14×unpow-prod-down *-un-lft-identity
12×pow-to-exp pow-exp
11×associate-*l* add-cbrt-cube
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
3×diff-log
2×pow-prod-down *-commutative distribute-lft-out--
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ flip-- flip-+ distribute-lft-out difference-of-squares
Counts
4 → 105
Calls
4 calls:
6.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
11.0ms
(* 2 (* (pow a 2) (pow b 2)))
151.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
9.0ms
(* (pow a 2) (pow b 2))

series179.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
35.0ms
(* 2 (* (pow a 2) (pow b 2)))
56.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
32.0ms
(* (pow a 2) (pow b 2))

simplify975.0ms

Counts
117 → 117
Iterations

Useful iterations: 2 (242.0ms)

IterNodesCost
01571770
13831595
215051379
done50001379

prune243.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes47.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02229
12829
done2829

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20641×body80valid