Details

Time bar (total: 4.8s)

sample41.0ms

Algorithm
intervals
Results
22.0ms646×body80valid

simplify59.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0258
1418
2678
31198
43098
514948
650018
done50018

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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))) 1.0)
0.0b
(* 4.0 (* b b))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite314.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube
7×add-cube-cbrt
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×diff-log sum-log
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ associate-*r* pow-exp associate--l+ *-commutative flip-- flip-+ distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 63
Calls
4 calls:
8.0ms
(+ (* a a) (* b b))
280.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
16.0ms
(* 4.0 (* b b))
9.0ms
(pow (+ (* a a) (* b b)) 2.0)

series290.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* a a) (* b b))
80.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
36.0ms
(* 4.0 (* b b))
144.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify38.0ms

Counts
75 → 75
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0338488
11360446
25001439
done5001439

prune170.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a 4) (* 4.0 (pow b 2)))
0.0b
(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
0.0b
(* 4.0 (pow b 2))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-log-exp
8×add-exp-log *-un-lft-identity associate-*r*
6×add-cube-cbrt
5×add-cbrt-cube
4×unpow-prod-down unswap-sqr
3×pow1 associate-*l* prod-exp
2×diff-log sum-log unpow2 sqr-pow
1×+-commutative pow-to-exp sub-neg flip3-- flip3-+ pow-exp associate--l+ *-commutative flip-- cbrt-unprod flip-+ distribute-lft-out-- difference-of-squares
Counts
3 → 54
Calls
3 calls:
11.0ms
(+ (pow a 4) (* 4.0 (pow b 2)))
62.0ms
(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
11.0ms
(* 4.0 (pow b 2))

series132.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(+ (pow a 4) (* 4.0 (pow b 2)))
59.0ms
(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
27.0ms
(* 4.0 (pow b 2))

simplify175.0ms

Counts
63 → 63
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0231330
1877307
24451303
35001303
done5001303

prune138.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b
(* 2.0 (* (pow a 2) (pow b 2)))
0.0b
(* 4.0 (* b b))
1.3b
(* (pow a 2) (pow b 2))

rewrite113.0ms

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:
50.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
27.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
15.0ms
(* 4.0 (* b b))
17.0ms
(* (pow a 2) (pow b 2))

series163.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
42.0ms
(* 2.0 (* (pow a 2) (pow b 2)))
25.0ms
(* 4.0 (* b b))
33.0ms
(* (pow a 2) (pow b 2))

simplify59.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0400683
11741575
25002568
done5002568

prune223.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
11.6b
(/ (- (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (* 1.0 1.0)) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))

rewrite454.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
16×times-frac
9×add-exp-log unpow-prod-down pow-unpow
7×pow1
6×add-cbrt-cube
5×distribute-lft-out difference-of-squares
4×associate-/r* associate-/l* add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
2×associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ div-inv
Counts
4 → 92
Calls
4 calls:
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
9.0ms
(pow (+ (* a a) (* b b)) 2.0)
423.0ms
(/ (- (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (* 1.0 1.0)) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))

series631.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(pow (+ (* a a) (* b b)) 2.0)
111.0ms
(pow (+ (* a a) (* b b)) 2.0)
115.0ms
(pow (+ (* a a) (* b b)) 2.0)
298.0ms
(/ (- (* (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (* 1.0 1.0)) (+ (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))

simplify53.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03341917
116041788
250021754
done50021754

prune291.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes151.0ms

Accuracy

86.7% (1.5b remaining)

Error of 1.5b against oracle of 0.1b and baseline of 11.3b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03216
13216
done3216

end0.0ms

sample1.2s

Algorithm
intervals
Results
735.0ms20589×body80valid