Details

Time bar (total: 7.3s)

sample67.0ms

Algorithm
intervals
Results
43.0ms651×body80valid

simplify64.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

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)
0.9b
(* (* b b) (+ 3.0 a))

rewrite139.0ms

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×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 distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
58.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
37.0ms
(* (* a a) (- 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
32.0ms
(* (* b b) (+ 3.0 a))

series330.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
61.0ms
(* (* a a) (- 1.0 a))
113.0ms
(pow (+ (* a a) (* b b)) 2.0)
37.0ms
(* (* b b) (+ 3.0 a))

simplify62.0ms

Counts
93 → 93

prune280.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
0.1b
(* (* a a) (- (* 1.0 1.0) (* a a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.9b
(* (* b b) (+ 3.0 a))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
23×add-cbrt-cube
16×*-un-lft-identity
15×pow1
12×add-sqr-sqrt
10×add-cube-cbrt
9×prod-exp cbrt-unprod
8×associate-*r*
6×associate-*r/ pow-prod-down
4×times-frac associate-/r* add-log-exp
3×cbrt-undiv distribute-rgt-in unpow-prod-down pow-unpow distribute-lft-in div-exp distribute-lft-out
2×sub-neg flip3-- flip3-+ associate-*l* associate-/r/ *-commutative flip-- flip-+ associate-/l/ unswap-sqr
1×pow-to-exp pow-pow frac-2neg pow-exp clear-num div-inv associate-/l* difference-of-squares sqr-pow
Counts
4 → 96
Calls
4 calls:
40.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
43.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (+ 3.0 a))

series371.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
89.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
114.0ms
(pow (+ (* a a) (* b b)) 2.0)
36.0ms
(* (* b b) (+ 3.0 a))

simplify79.0ms

Counts
108 → 108

prune340.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 a) (- (* 1.0 1.0) (* a a)))
0.1b
(/ (* a a) (/ (+ 1.0 a) (- (* 1.0 1.0) (* a a))))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.9b
(* (* b b) (+ 3.0 a))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
70×times-frac
63×*-un-lft-identity
36×add-sqr-sqrt
35×add-cube-cbrt
26×associate-/r*
24×add-exp-log
23×add-cbrt-cube
14×distribute-lft-out
13×difference-of-squares
10×pow1
7×cbrt-undiv div-exp associate-/r/
5×prod-exp cbrt-unprod associate-/l*
4×associate-*r* div-inv add-log-exp
3×unpow-prod-down pow-unpow flip3-- pow-prod-down flip--
2×frac-2neg flip3-+ associate-*r/ clear-num flip-+ associate-/l/
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in associate-*l* pow-exp *-commutative unswap-sqr sqr-pow
Counts
4 → 145
Calls
4 calls:
27.0ms
(/ (+ 1.0 a) (- (* 1.0 1.0) (* a a)))
33.0ms
(/ (* a a) (/ (+ 1.0 a) (- (* 1.0 1.0) (* a a))))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (+ 3.0 a))

series331.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (+ 1.0 a) (- (* 1.0 1.0) (* a a)))
130.0ms
(/ (* a a) (/ (+ 1.0 a) (- (* 1.0 1.0) (* a a))))
118.0ms
(pow (+ (* a a) (* b b)) 2.0)
40.0ms
(* (* b b) (+ 3.0 a))

simplify95.0ms

Counts
157 → 157

prune554.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* b b) (+ 3.0 a))
0.9b
(* (* b b) (+ 3.0 a))
9.1b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
9.1b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
2×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 78
Calls
4 calls:
31.0ms
(* (* b b) (+ 3.0 a))
32.0ms
(* (* b b) (+ 3.0 a))
63.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
66.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* b b) (+ 3.0 a))
42.0ms
(* (* b b) (+ 3.0 a))
194.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
195.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify43.0ms

Counts
90 → 90

prune332.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes168.0ms

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

sample3.0s

Algorithm
intervals
Results
2.5s20678×body80valid