Details

Time bar (total: 15.8s)

sample112.0ms

Algorithm
intervals
Results
79.0ms655×body80valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done5000
41716
3492
2161
153
019

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

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)))

rewrite185.0ms

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×pow-unpow unpow-prod-down
2×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out sqr-pow
Counts
4 → 79
Calls
4 calls:
71.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
43.0ms
(* (* a a) (+ 1.0 a))
16.0ms
(pow (+ (* a a) (* b b)) 2.0)
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
104.0ms
(* (* a a) (+ 1.0 a))
125.0ms
(pow (+ (* a a) (* b b)) 2.0)
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.7s

Counts
91 → 91
Iterations
IterNodes
done5000
23892
1552
0175

prune564.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (- 1.0 (* 3.0 a)) (pow b 2))
0.7b
(* (- 1.0 (* 3.0 a)) (pow b 2))
7.6b
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))
7.6b
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
16×associate-*r*
14×add-exp-log
12×*-un-lft-identity add-cube-cbrt
8×unpow-prod-down add-cbrt-cube unswap-sqr
6×pow1 associate-*l* prod-exp sqrt-prod
4×sqrt-div associate-*l/ unpow2 add-log-exp sqr-pow
2×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 pow-exp *-commutative cbrt-unprod flip-+ flip--
Counts
4 → 88
Calls
4 calls:
27.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
34.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
131.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))
103.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

series582.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
96.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
227.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))
166.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

simplify885.0ms

Counts
100 → 100
Iterations
IterNodes
done5002
21558
1311
0125

prune865.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (- 1.0 (* 3.0 a)) (pow b 2))
7.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ 1.0 a)))))))
7.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ 1.0 a)))))))
7.6b
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

rewrite611.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×add-exp-log sqrt-prod
8×associate-*r*
7×pow1
6×add-cbrt-cube sqrt-div
4×unpow-prod-down add-log-exp unswap-sqr
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*l* prod-exp flip-+
2×associate-*l/ unpow2 sqr-pow
1×pow-to-exp flip3-- pow-exp *-commutative cbrt-unprod flip--
Counts
4 → 74
Calls
4 calls:
24.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
53.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ 1.0 a)))))))
71.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ 1.0 a)))))))
460.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

series785.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
235.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ 1.0 a)))))))
229.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* b (* b (- 1.0 (* a 3.0)))) (* a (* a (+ 1.0 a)))))))
244.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

simplify952.0ms

Counts
86 → 86
Iterations
IterNodes
done5000
22159
1455
0182

prune943.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 2 (* a a))
1.9b
(* (pow b 2) (* 2 (* a a)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
21×prod-exp
16×add-cbrt-cube
11×associate-*l*
9×cbrt-unprod
7×pow1
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
3×pow-to-exp unpow-prod-down pow-prod-down pow-exp
2×associate-*r* *-commutative add-log-exp
1×unpow2 unswap-sqr sqr-pow
Counts
2 → 48
Calls
2 calls:
12.0ms
(* 2 (* a a))
40.0ms
(* (pow b 2) (* 2 (* a a)))

series69.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(* 2 (* a a))
38.0ms
(* (pow b 2) (* 2 (* a a)))

simplify623.0ms

Counts
54 → 54
Iterations
IterNodes
done5001
21204
1208
074

prune180.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done56
356
254
151
037

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.4s20671×body80valid