Details

Time bar (total: 7.0s)

sample90.0ms

Algorithm
intervals
Results
46.0ms653×body80valid

simplify84.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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)
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite140.0ms

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:
59.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
32.0ms
(* (* a a) (+ 1.0 a))
18.0ms
(pow (+ (* a a) (* b b)) 2.0)
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* a a) (+ 1.0 a))
115.0ms
(pow (+ (* a a) (* b b)) 2.0)
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify62.0ms

Counts
91 → 91

prune261.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
11.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
11.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite186.0ms

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:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
61.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
65.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
191.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
187.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify45.0ms

Counts
92 → 92

prune348.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (- 1.0 (* 3.0 a)))
11.9b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
12.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
12.5b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
4×cbrt-div add-log-exp
3×flip3-+ associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod flip-+
2×distribute-rgt-in sub-neg distribute-lft-in pow1/3 sqrt-div associate-*r/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 66
Calls
4 calls:
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
61.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
31.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
38.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series654.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
187.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
204.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
207.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify48.0ms

Counts
78 → 78

prune453.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 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
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
2.4b
(* (pow a 2) (pow b 2))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
16×unswap-sqr
15×add-exp-log
14×unpow-prod-down
10×unpow2 add-log-exp sqr-pow
9×*-un-lft-identity prod-exp
8×associate-*r* associate-*l*
7×add-cube-cbrt
6×pow-to-exp pow-exp
5×add-cbrt-cube
4×sum-log
3×pow1
2×+-commutative flip3-+ flip-+
1×associate-+r+ pow-prod-down *-commutative cbrt-unprod distribute-lft-out
Counts
3 → 76
Calls
3 calls:
14.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
35.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
23.0ms
(* (pow a 2) (pow b 2))

series153.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
56.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
35.0ms
(* (pow a 2) (pow b 2))

simplify47.0ms

Counts
85 → 85

prune223.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.4s20825×body80valid