Details

Time bar (total: 27.1s)

sample109.0ms

Algorithm
intervals
Results
72.0ms640×body80valid

simplify3.4s

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

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)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite129.0ms

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:
60.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
26.0ms
(* (* a a) (+ 1.0 a))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
80.0ms
(* (* a a) (+ 1.0 a))
186.0ms
(pow (+ (* a a) (* b b)) 2.0)
91.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.3s

Counts
112 → 112
Iterations
IterNodes
done5000
24499
1620
0201

prune788.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
11.5b
(sqrt (pow (+ (* a a) (* b b)) 2.0))
11.5b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×sqrt-prod
13×*-un-lft-identity add-cube-cbrt
11×unpow-prod-down
10×pow1 add-exp-log
9×add-cbrt-cube
6×rem-sqrt-square prod-diff
5×distribute-rgt-in distribute-lft-in sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg sqrt-pow1 pow1/2 associate-*r/
1×pow-to-exp pow-pow flip3-- associate-*l* pow-exp *-commutative flip-- unswap-sqr
Counts
4 → 94
Calls
4 calls:
15.0ms
(pow (+ (* a a) (* b b)) 2.0)
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
25.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
15.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series724.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(pow (+ (* a a) (* b b)) 2.0)
72.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
237.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
236.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.4s

Counts
106 → 106
Iterations
IterNodes
done5001
22235
1386
0145

prune948.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.7b
(* (* b b) (- 1.0 (* 3.0 a)))
11.5b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
10×pow1 add-exp-log
9×add-cbrt-cube
7×unpow-prod-down sqrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square pow-unpow associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×sub-neg associate-*r/
1×pow-to-exp pow-pow sqrt-pow1 flip3-- pow1/2 associate-*l* pow-exp *-commutative fma-udef flip-- unswap-sqr
Counts
4 → 83
Calls
4 calls:
1.0ms
(fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
15.0ms
(pow (+ (* a a) (* b b)) 2.0)
59.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
28.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series807.0ms

Counts
4 → 12
Calls
4 calls:
310.0ms
(fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
145.0ms
(pow (+ (* a a) (* b b)) 2.0)
91.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
260.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify3.9s

Counts
95 → 95
Iterations
IterNodes
done5001
22784
1495
0183

prune731.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
8.0b
(sqrt (fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
11.5b
(sqrt (pow (+ (* a a) (* b b)) 2.0))
11.5b
(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
20×sqrt-prod
16×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×rem-sqrt-square unpow-prod-down
6×pow1
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u add-log-exp sqr-pow
Counts
4 → 72
Calls
4 calls:
1.0ms
(sqrt (fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
1.0ms
(sqrt (fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
13.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
21.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
470.0ms
(sqrt (fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
504.0ms
(sqrt (fma (fma b b (* a (* a 1.0))) (sqrt (pow (+ (* a a) (* b b)) 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
224.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))
208.0ms
(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.9s

Counts
84 → 84
Iterations
IterNodes
done5000
34230
2838
1267
0119

prune726.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes401.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done34
134
025

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.8s20149×body80valid