Details

Time bar (total: 18.5s)

sample73.0ms

Algorithm
intervals
Results
41.0ms665×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01217
12517
24017
36617
412017
542617
6350717
done500117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a a) (* b b))
0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b
(* 4.0 (* b b))
0.4b
(pow (+ (* a a) (* b b)) 2.0)

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×+-commutative flip3-+ sum-log flip-+
1×pow-to-exp pow-pow associate-*r* pow-exp *-commutative unswap-sqr sqr-pow
Counts
4 → 58
Calls
4 calls:
18.0ms
(+ (* a a) (* b b))
85.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
19.0ms
(* 4.0 (* b b))
18.0ms
(pow (+ (* a a) (* b b)) 2.0)

series345.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (* a a) (* b b))
100.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
32.0ms
(* 4.0 (* b b))
174.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify1.6s

Counts
70 → 70
Iterations

Useful iterations: 2 (429.0ms)

IterNodesCost
0117931
1383848
22181778
done5001778

prune254.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
2.7b
(* (pow a 2) (pow b 2))

rewrite171.0ms

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:
15.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
37.0ms
(* 2 (* (pow a 2) (pow b 2)))
70.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
45.0ms
(* (pow a 2) (pow b 2))

series239.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
52.0ms
(* 2 (* (pow a 2) (pow b 2)))
70.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
43.0ms
(* (pow a 2) (pow b 2))

simplify2.2s

Counts
113 → 113
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01461649
13861443
224081245
done50021237

prune434.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (* (pow a 2) (pow b 2)))
0.0b
(* 4.0 (* b b))
0.0b
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
2.7b
(* (pow a 2) (pow b 2))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
31×prod-exp
27×add-sqr-sqrt
17×unswap-sqr
16×add-cbrt-cube
14×unpow-prod-down associate-*l*
12×pow-to-exp pow-exp
11×pow1
10×add-cube-cbrt *-un-lft-identity associate-*r* unpow2 sqr-pow
9×add-log-exp
7×cbrt-unprod
5×pow-prod-down
3×sum-log *-commutative
1×+-commutative associate-+l+ flip3-+ flip-+
Counts
4 → 108
Calls
4 calls:
42.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
19.0ms
(* 4.0 (* b b))
65.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
21.0ms
(* (pow a 2) (pow b 2))

series253.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
29.0ms
(* 4.0 (* b b))
96.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
62.0ms
(* (pow a 2) (pow b 2))

simplify2.3s

Counts
120 → 120
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01601554
14321418
228021118
done50021106

prune394.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* b b))
0.3b
(pow (+ (* a a) (* b b)) (* 2 2.0))
0.4b
(pow (+ (* a a) (* b b)) 2.0)
34.8b
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 4.0) (pow b 4))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite456.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
13×add-exp-log
11×pow1 add-cbrt-cube
9×times-frac
6×unpow-prod-down
4×pow-unpow add-log-exp
3×associate-*l* pow-prod-down prod-exp associate-/r* cbrt-unprod associate-/l*
2×pow-to-exp flip3-- pow-pow pow-exp associate-/r/ flip-- associate-/l/ sqr-pow
1×cbrt-undiv frac-2neg div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
4 → 83
Calls
4 calls:
33.0ms
(* 4.0 (* b b))
21.0ms
(pow (+ (* a a) (* b b)) (* 2 2.0))
19.0ms
(pow (+ (* a a) (* b b)) 2.0)
381.0ms
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 4.0) (pow b 4))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series696.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* 4.0 (* b b))
157.0ms
(pow (+ (* a a) (* b b)) (* 2 2.0))
163.0ms
(pow (+ (* a a) (* b b)) 2.0)
329.0ms
(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 4.0) (pow b 4))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify2.0s

Counts
95 → 95
Iterations

Useful iterations: 2 (492.0ms)

IterNodesCost
01782489
15072399
229032211
done50002211

prune359.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01419
11819
done1819

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.0s20473×body80valid