Details

Time bar (total: 24.0s)

sample84.0ms

Algorithm
intervals
Results
51.0ms709×body80valid

simplify6.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
01931
15529
217828
354528
4167228
5479728
done500028

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
17×pow1 add-exp-log
16×add-sqr-sqrt add-cbrt-cube
14×*-un-lft-identity
12×add-cube-cbrt
10×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×unpow-prod-down pow-unpow flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×pow-to-exp pow-pow pow-exp distribute-lft-out sqr-pow
Counts
4 → 106
Calls
4 calls:
122.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
48.0ms
(* (* a a) (+ 1.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
93.0ms
(* (* a a) (+ 1.0 a))
146.0ms
(pow (+ (* a a) (* b b)) 2.0)
82.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.5s

Counts
118 → 118
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02381961
17001783
229631607
done50001596

prune537.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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
(pow (+ (* a a) (* b b)) 2.0)
0.4b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-*r/
17×pow1 add-exp-log
16×add-cbrt-cube
15×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
10×distribute-rgt-in distribute-lft-in
7×associate-*r* associate-*l* pow-prod-down prod-exp cbrt-unprod
6×prod-diff
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow flip3-- *-commutative flip--
2×sub-neg unswap-sqr
1×pow-to-exp pow-pow pow-exp sqr-pow
Counts
4 → 106
Calls
4 calls:
166.0ms
(* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))
31.0ms
(* a (* a (+ 1.0 a)))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* 4.0 (+ (* a (* a (+ 1.0 a))) (* (* b b) (- 1.0 (* 3.0 a)))))
62.0ms
(* a (* a (+ 1.0 a)))
148.0ms
(pow (+ (* a a) (* b b)) 2.0)
67.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.3s

Counts
118 → 118
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02401959
17011791
227961603
done50021594

prune595.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* b b) (- 1.0 (* 3.0 a)))
25.5b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
25.5b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
25.5b
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
8×add-sqr-sqrt associate-*r/
7×add-cube-cbrt *-un-lft-identity
6×cbrt-div prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg
1×associate-*l* *-commutative unswap-sqr
Counts
4 → 72
Calls
4 calls:
45.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
18.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
37.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
27.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

series725.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
234.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
202.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))
220.0ms
(cbrt (* (* b b) (- 1.0 (* 3.0 a))))

simplify3.1s

Counts
84 → 84
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01621874
14091809
212631622
345901422
done50001413

prune548.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)) (cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))
10.3b
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))
10.3b
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))
10.3b
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u swap-sqr associate-*r* associate-*l* add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
25.0ms
(* (cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)) (cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))
4.0ms
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))
3.0ms
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))
5.0ms
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
295.0ms
(* (cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)) (cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0)))
266.0ms
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))
294.0ms
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))
233.0ms
(cbrt (* (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0))

simplify2.2s

Counts
78 → 78
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01292655
13092450
29502107
334161723
done50001716

prune417.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes114.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02354
13354
done3354

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s20533×body80valid