Details

Time bar (total: 17.4s)

sample88.0ms

Algorithm
intervals
Results
65.0ms642×body80valid

simplify1.5s

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

prune17.0ms

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)
0.8b
(* (* 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×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:
48.0ms
(+ (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))
15.0ms
(pow (+ (* a a) (* b b)) 2.0)
43.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
101.0ms
(* (* a a) (+ 1.0 a))
125.0ms
(pow (+ (* a a) (* b b)) 2.0)
55.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.6s

Counts
91 → 91
Iterations
IterNodes
done5000
23892
1552
0175

prune649.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (- 1.0 (* 3.0 a)) (pow b 2)))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.8b
(* (- 1.0 (* 3.0 a)) (pow b 2))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×add-exp-log
12×*-un-lft-identity associate-*r*
11×add-cbrt-cube
10×pow1 add-cube-cbrt
7×unpow-prod-down
6×prod-exp add-log-exp
5×unswap-sqr
4×associate-*l* cbrt-unprod
3×pow-unpow pow-prod-down sqr-pow
2×distribute-rgt-in pow-to-exp associate-+r+ distribute-lft-in flip3-+ associate-*l/ pow-exp associate-*r/ *-commutative flip-+ unpow2
1×+-commutative sum-log pow-pow flip3-- flip-- distribute-lft-out
Counts
4 → 83
Calls
4 calls:
66.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (- 1.0 (* 3.0 a)) (pow b 2)))))
26.0ms
(* (* a a) (+ 1.0 a))
8.0ms
(pow (+ (* a a) (* b b)) 2.0)
18.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))

series464.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (- 1.0 (* 3.0 a)) (pow b 2)))))
74.0ms
(* (* a a) (+ 1.0 a))
176.0ms
(pow (+ (* a a) (* b b)) 2.0)
67.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))

simplify2.2s

Counts
95 → 95
Iterations
IterNodes
done5002
23295
1536
0186

prune734.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize128.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (- 1.0 (* 3.0 a)) (pow b 2))
0.8b
(* (- 1.0 (* 3.0 a)) (pow b 2))
6.7b
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))
6.7b
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

rewrite279.0ms

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:
19.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
18.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
116.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))
123.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

series566.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
73.0ms
(* (- 1.0 (* 3.0 a)) (pow b 2))
202.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))
226.0ms
(sqrt (+ (pow (+ (pow b 2) (* a a)) 2.0) (* 4.0 (+ (* (* a (+ 1.0 a)) a) (* (- 1.0 (* 3.0 a)) (pow b 2))))))

simplify918.0ms

Counts
100 → 100
Iterations
IterNodes
done5002
21558
1311
0125

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* (pow b 2) (* 2 (* a a))) (pow b 4))
2.5b
(* (pow b 2) (* 2 (* a a)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
18×prod-exp
11×add-cbrt-cube
8×associate-*l*
6×cbrt-unprod
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
3×pow-to-exp unpow-prod-down pow-exp
2×pow1
1×+-commutative sum-log flip3-+ associate-*r* *-commutative flip-+ unpow2 sqr-pow
Counts
2 → 40
Calls
2 calls:
50.0ms
(+ (* (pow b 2) (* 2 (* a a))) (pow b 4))
51.0ms
(* (pow b 2) (* 2 (* a a)))

series151.0ms

Counts
2 → 6
Calls
2 calls:
86.0ms
(+ (* (pow b 2) (* 2 (* a a))) (pow b 4))
64.0ms
(* (pow b 2) (* 2 (* a a)))

simplify822.0ms

Counts
46 → 46
Iterations
IterNodes
done5001
21442
1253
086

prune223.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes266.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done29
129
021

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.2s20748×body80valid