Details

Time bar (total: 13.0s)

sample54.0ms

Algorithm
intervals
Results
36.0ms660×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
214031
334431
484131
5185531
6375431
done500131

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

rewrite59.0ms

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:
24.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
15.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(+ (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))
109.0ms
(pow (+ (* a a) (* b b)) 2.0)
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify994.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (345.0ms)

IterNodesCost
01751540
14901431
220021287
done50011287

prune251.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
7.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.5b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite87.0ms

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:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
28.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
32.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series479.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
57.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
184.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
182.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify713.0ms

Counts
92 → 92
Iterations

Useful iterations: done (709.0ms)

IterNodesCost
01202304
13292090
212511892
done50021888

prune333.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
19.5b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
16.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series529.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
161.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
161.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
155.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.5s

Counts
82 → 82
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01101276
12601259
28841133
337441124
done50011124

prune302.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
0.0b
(* 2 (* (pow a 2) (pow b 2)))
3.0b
(* (pow a 2) (pow b 2))

rewrite177.0ms

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))))
147.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
10.0ms
(* 2 (* (pow a 2) (pow b 2)))
9.0ms
(* (pow a 2) (pow b 2))

series184.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
54.0ms
(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
40.0ms
(* 2 (* (pow a 2) (pow b 2)))
34.0ms
(* (pow a 2) (pow b 2))

simplify804.0ms

Counts
117 → 117
Iterations

Useful iterations: done (801.0ms)

IterNodesCost
01571770
13831595
215021379
done50001377

prune251.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes151.0ms

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 (1.0ms)

IterNodesCost
02163
12963
done2963

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s20612×body80valid