Details

Time bar (total: 16.3s)

sample56.0ms

Algorithm
intervals
Results
33.0ms631×body80valid

simplify4.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
01931
15529
217828
354528
4167228
5479728
done500028

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)
1.2b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
65.0ms
(+ (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))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
34.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series329.0ms

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))
108.0ms
(pow (+ (* a a) (* b b)) 2.0)
52.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.1s

Counts
112 → 112
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02011802
15401621
220541446
done50001435

prune349.0ms

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
(- 1.0 (* 3.0 a))
0.1b
(* (* a a) (+ 1.0 a))
0.2b
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
1.2b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×prod-diff
7×associate-*r*
6×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×sub-neg fma-neg
2×flip3-- associate-*l* *-commutative flip-- unswap-sqr
1×flip3-+ diff-log flip-+ fma-udef distribute-lft-out
Counts
4 → 89
Calls
4 calls:
6.0ms
(- 1.0 (* 3.0 a))
30.0ms
(* (* a a) (+ 1.0 a))
0.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
32.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- 1.0 (* 3.0 a))
53.0ms
(* (* a a) (+ 1.0 a))
124.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify941.0ms

Counts
101 → 101
Iterations

Useful iterations: done (938.0ms)

IterNodesCost
01601630
14241441
215711233
done50011210

prune315.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* b b) (- 1.0 (* 3.0 a)))
1.2b
(* (* b b) (- 1.0 (* 3.0 a)))
9.0b
(sqrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
9.0b
(sqrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity prod-diff
10×distribute-rgt-in distribute-lft-in
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg associate-*r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 96
Calls
4 calls:
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(sqrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
2.0ms
(sqrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))

series537.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
57.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
215.0ms
(sqrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
213.0ms
(sqrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))

simplify2.3s

Counts
108 → 108
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01322364
13262206
29661964
333841880
done50001748

prune478.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* b b) (- 1.0 (* 3.0 a)))
9.6b
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
9.6b
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
9.6b
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log cbrt-prod add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 72
Calls
4 calls:
31.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
1.0ms
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
1.0ms
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))

series809.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
247.0ms
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
253.0ms
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))
251.0ms
(cbrt (fma (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (pow b 2)) (* 2 (/ 2.0 2)))))

simplify2.1s

Counts
84 → 84
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01462699
13532679
210452394
336682124
done50002082

prune484.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes89.0ms

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
02144
12844
done2844

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s20101×body80valid