Details

Time bar (total: 24.1s)

sample137.0ms

Algorithm
intervals
Results
94.0ms709×body80valid

simplify5.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
01931
15529
217828
354528
4167228
5479728
done500028

prune12.0ms

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
(+ (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
(* (* b b) (- 1.0 (* 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite169.0ms

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:
69.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms
(* (* a a) (+ 1.0 a))
38.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)

series515.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
99.0ms
(* (* a a) (+ 1.0 a))
96.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
170.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify1.7s

Counts
112 → 112
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02011802
15401621
220511446
done50011435

prune560.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 2 (pow a 2) (pow b 2))
0.1b
(fma (pow b 2) (fma 2 (pow a 2) (pow b 2)) (pow a 4))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(fma 2 (pow a 2) (pow b 2))
1.0ms
(fma (pow b 2) (fma 2 (pow a 2) (pow b 2)) (pow a 4))

series190.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(fma 2 (pow a 2) (pow b 2))
121.0ms
(fma (pow b 2) (fma 2 (pow a 2) (pow b 2)) (pow a 4))

simplify2.9s

Counts
26 → 26
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
037395
167392
2173340
3626340
43425340
done5000340

prune169.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
1.1b
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
16×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt associate-*r*
7×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
6×prod-diff
5×associate-*l*
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×fma-udef distribute-lft-out
Counts
4 → 97
Calls
4 calls:
135.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
39.0ms
(* (* a a) (+ 1.0 a))
61.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series484.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
117.0ms
(* (* a a) (+ 1.0 a))
114.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
113.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify2.2s

Counts
109 → 109
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02151884
16451750
228731559
done50011548

prune663.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (fma 4.0 (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)) 3)
0.3b
(* (* b b) (- 1.0 (* 3.0 a)))
0.3b
(pow (fma a a (* b b)) 2.0)
32.5b
(cbrt (pow (fma 4.0 (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)) 3))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
11×pow1 add-exp-log
10×add-cbrt-cube
9×unpow-prod-down
6×pow-unpow cube-prod prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×cube-mult pow-to-exp sub-neg pow-pow unpow3 associate-*r/ pow-exp
1×flip3-- pow1/3 associate-*l* *-commutative flip-- rem-cbrt-cube rem-cube-cbrt unswap-sqr
Counts
4 → 100
Calls
4 calls:
6.0ms
(pow (fma 4.0 (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)) 3)
45.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
3.0ms
(pow (fma a a (* b b)) 2.0)
3.0ms
(cbrt (pow (fma 4.0 (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
584.0ms
(pow (fma 4.0 (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)) 3)
83.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
226.0ms
(pow (fma a a (* b b)) 2.0)
169.0ms
(cbrt (pow (fma 4.0 (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)) 3))

simplify1.6s

Counts
112 → 112
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02073074
14972824
215882423
done50012410

prune560.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes162.0ms

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

sample4.7s

Algorithm
intervals
Results
3.9s20340×body80valid