Details

Time bar (total: 25.5s)

sample157.0ms

Algorithm
intervals
Results
109.0ms642×body80valid

simplify4.3s

Counts
1 → 1
Iterations
IterNodes
done5000
42195
3588
2179
155
019

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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)
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
99.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
33.0ms
(* (* a a) (+ 1.0 a))
16.0ms
(pow (+ (* a a) (* b b)) 2.0)
25.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
79.0ms
(* (* a a) (+ 1.0 a))
145.0ms
(pow (+ (* a a) (* b b)) 2.0)
73.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.1s

Counts
112 → 112
Iterations
IterNodes
done5000
24499
1620
0201

prune753.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

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)
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
23×add-cbrt-cube
18×add-sqr-sqrt
16×*-un-lft-identity
15×pow1
12×add-cube-cbrt
9×prod-exp cbrt-unprod
8×distribute-rgt-in distribute-lft-in prod-diff
7×associate-*r*
6×pow-prod-down associate-*r/
5×associate-/r* times-frac
4×expm1-log1p-u sub-neg flip3-- log1p-expm1-u flip-- add-log-exp
3×cbrt-undiv pow-unpow unpow-prod-down div-exp difference-of-squares
2×associate-*l* associate-/r/ *-commutative distribute-lft-out-- unswap-sqr associate-/l/
1×pow-to-exp clear-num pow-pow frac-2neg pow-exp div-inv associate-/l* sqr-pow
Counts
4 → 115
Calls
4 calls:
37.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a))
42.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
16.0ms
(pow (+ (* a a) (* b b)) 2.0)
36.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a))
101.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
184.0ms
(pow (+ (* a a) (* b b)) 2.0)
72.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify894.0ms

Counts
127 → 127
Iterations
IterNodes
done5000
1725
0232

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize104.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
6.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
6.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt pow1
14×add-cbrt-cube add-exp-log
12×*-un-lft-identity prod-diff add-cube-cbrt
10×distribute-rgt-in distribute-lft-in
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg sqrt-div associate-*r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 associate-*l* *-commutative flip-+ flip-- unswap-sqr
Counts
4 → 100
Calls
4 calls:
35.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
48.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
75.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
70.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series707.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
88.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
269.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
255.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify2.6s

Counts
112 → 112
Iterations
IterNodes
done5001
22488
1411
0143

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize201.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.2b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-+ add-cbrt-cube add-exp-log flip-+ log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
78.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
52.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
30.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
46.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
293.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
260.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
260.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
339.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify1.5s

Counts
74 → 74
Iterations
IterNodes
done5000
21052
1293
0122

prune952.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes696.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done29
129
022

end0.0ms

sample4.5s

Algorithm
intervals
Results
3.7s20748×body80valid