Details

Time bar (total: 12.5s)

sample59.0ms

Algorithm
intervals
Results
36.0ms699×body80valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216031
345131
4122331
5246931
6461831
done500131

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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)))

rewrite128.0ms

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:
56.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
30.0ms
(* (* a a) (+ 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* a a) (+ 1.0 a))
107.0ms
(pow (+ (* a a) (* b b)) 2.0)
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify844.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (309.0ms)

IterNodesCost
01751540
14791431
218381287
done50001287

prune245.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×add-exp-log
12×*-un-lft-identity
11×associate-*r* add-cbrt-cube
10×pow1 add-cube-cbrt
7×unpow-prod-down
6×prod-exp add-log-exp
5×associate-*l* unswap-sqr
4×cbrt-unprod
3×distribute-rgt-in pow-unpow distribute-lft-in pow-prod-down sqr-pow
2×pow-to-exp sub-neg associate-+r+ flip3-+ associate-*r/ associate-*l/ pow-exp *-commutative flip-+ unpow2
1×+-commutative flip3-- pow-pow sum-log flip-- distribute-lft-out
Counts
4 → 85
Calls
4 calls:
55.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (+ 1.0 a) (pow a 2)) (* (* b b) (- 1.0 (* 3.0 a))))))
26.0ms
(* (+ 1.0 a) (pow a 2))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (+ 1.0 a) (pow a 2)) (* (* b b) (- 1.0 (* 3.0 a))))))
49.0ms
(* (+ 1.0 a) (pow a 2))
109.0ms
(pow (+ (* a a) (* b b)) 2.0)
54.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify840.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (286.0ms)

IterNodesCost
01881607
14811504
216781343
done50011343

prune295.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* b b) (- 1.0 (* 3.0 a)))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
4×add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
29.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
11.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series526.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
158.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
156.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
161.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify1.6s

Counts
82 → 82
Iterations

Useful iterations: 3 (703.0ms)

IterNodesCost
01101276
12561259
27561133
327381124
done50021124

prune313.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

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)))
1.4b
(* (pow a 2) (pow b 2))

rewrite98.0ms

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:
36.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
13.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
25.0ms
(* 2 (* (pow a 2) (pow b 2)))
20.0ms
(* (pow a 2) (pow b 2))

series188.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
55.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
41.0ms
(* 2 (* (pow a 2) (pow b 2)))
33.0ms
(* (pow a 2) (pow b 2))

simplify799.0ms

Counts
113 → 113
Iterations

Useful iterations: done (796.0ms)

IterNodesCost
01461649
13731431
212391245
done50011231

prune235.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes78.0ms

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
02131
12931
done2931

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20523×body80valid