Details

Time bar (total: 22.3s)

sample120.0ms

Algorithm
intervals
Results
77.0ms693×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216131
348631
4164531
done500131

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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)
1.4b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite216.0ms

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×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 sqr-pow
Counts
4 → 79
Calls
4 calls:
83.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
56.0ms
(* (* a a) (+ 1.0 a))
12.0ms
(pow (+ (* a a) (* b b)) 2.0)
63.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
93.0ms
(* (* a a) (+ 1.0 a))
158.0ms
(pow (+ (* a a) (* b b)) 2.0)
68.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.3s

Counts
91 → 91
Iterations

Useful iterations: 2 (833.0ms)

IterNodesCost
01751540
15511441
238261287
done50001287

prune451.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
2.2b
(* (pow a 2) (pow b 2))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
62.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
24.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
37.0ms
(* 2 (* (pow a 2) (pow b 2)))
26.0ms
(* (pow a 2) (pow b 2))

series231.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
70.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
45.0ms
(* 2 (* (pow a 2) (pow b 2)))
53.0ms
(* (pow a 2) (pow b 2))

simplify2.0s

Counts
113 → 113
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01461649
13861443
224091247
done50001233

prune390.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
1.4b
(* (* b b) (- 1.0 (* 3.0 a)))
2.2b
(* (pow a 2) (pow b 2))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
18×unswap-sqr
16×add-cbrt-cube
15×associate-*r* prod-exp
14×pow1 unpow-prod-down
12×*-un-lft-identity
10×add-cube-cbrt associate-*l* unpow2 sqr-pow
7×pow-prod-down cbrt-unprod
6×pow-to-exp pow-exp add-log-exp
4×associate-*r/
3×distribute-rgt-in sub-neg distribute-lft-in *-commutative
2×flip3-- flip--
1×flip3-+ diff-log flip-+ distribute-lft-out
Counts
4 → 112
Calls
4 calls:
6.0ms
(- 1.0 (* 3.0 a))
40.0ms
(* (* a a) (+ 1.0 a))
56.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
26.0ms
(* (pow a 2) (pow b 2))

series256.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- 1.0 (* 3.0 a))
86.0ms
(* (* a a) (+ 1.0 a))
70.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
50.0ms
(* (pow a 2) (pow b 2))

simplify4.9s

Counts
124 → 124
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
01771371
15081253
242571015
done50001015

prune599.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.4b
(* (* b b) (- 1.0 (* 3.0 a)))
27.9b
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
29×unpow-prod-down
20×cbrt-prod
18×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
14×cube-prod
12×add-exp-log
10×pow1 add-cbrt-cube
7×sqr-pow
6×pow-unpow
5×pow-exp
4×add-log-exp
3×pow-to-exp associate-*r* pow-prod-down prod-exp cbrt-unprod
2×distribute-rgt-in cube-mult sub-neg pow-pow distribute-lft-in unpow3 associate-*r/
1×flip3-- pow1/3 associate-*l* *-commutative flip-- rem-cbrt-cube rem-cube-cbrt unswap-sqr
Counts
4 → 104
Calls
4 calls:
34.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
38.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
26.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series639.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 3)
179.0ms
(pow (+ (* a a) (* b b)) 2.0)
77.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
220.0ms
(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify2.5s

Counts
116 → 116
Iterations

Useful iterations: 2 (701.0ms)

IterNodesCost
01691990
14961729
228561579
done50011579

prune418.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes177.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
12731
done2731

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.9s20552×body80valid