Details

Time bar (total: 7.1s)

sample10.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
057
176
done76

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) 1.0)
13.8b
(/ x (+ (* x x) 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 45
Calls
2 calls:
3.0ms
(+ (* x x) 1.0)
6.0ms
(/ x (+ (* x x) 1.0))

series90.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(+ (* x x) 1.0)
59.0ms
(/ x (+ (* x x) 1.0))

simplify1.3s

Counts
51 → 51
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
089580
1204497
2616448
32840448
done5001448

prune100.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (fma x x 1.0)))
0.0b
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
13.8b
(sqrt (fma x x 1.0))
13.8b
(sqrt (fma x x 1.0))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
30×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×pow1 div-exp
8×prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×rec-exp pow-flip sqrt-pow1 pow1/2 1-exp div-inv associate-/l*
2×rem-sqrt-square
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 162
Calls
4 calls:
3.0ms
(/ 1 (sqrt (fma x x 1.0)))
29.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
1.0ms
(sqrt (fma x x 1.0))
1.0ms
(sqrt (fma x x 1.0))

series259.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ 1 (sqrt (fma x x 1.0)))
70.0ms
(* (/ 1 (sqrt (fma x x 1.0))) (/ x (sqrt (fma x x 1.0))))
55.0ms
(sqrt (fma x x 1.0))
50.0ms
(sqrt (fma x x 1.0))

simplify792.0ms

Counts
174 → 174
Iterations

Useful iterations: 2 (256.0ms)

IterNodesCost
02092888
15762505
218022049
done50012049

prune287.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (pow x 5))
0.9b
(/ 1.0 (pow x 3))
20.7b
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
912×times-frac
655×add-sqr-sqrt
636×*-un-lft-identity
611×add-cube-cbrt
522×associate-+l+
520×prod-diff
144×unpow-prod-down
132×cube-prod
57×div-inv
50×sqr-pow
43×cube-mult unpow3
21×fma-def
19×associate-/r*
15×difference-of-squares
13×add-exp-log
8×add-log-exp
7×add-cbrt-cube
6×div-exp associate-/l* distribute-lft-out--
4×distribute-lft-out
3×pow1 expm1-log1p-u frac-add log1p-expm1-u
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num sum-log
1×+-commutative associate-+l- sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 679
Calls
3 calls:
3.0ms
(/ 1.0 (pow x 5))
4.0ms
(/ 1.0 (pow x 3))
320.0ms
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

series140.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(/ 1.0 (pow x 5))
35.0ms
(/ 1.0 (pow x 3))
52.0ms
(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

simplify1.2s

Counts
688 → 688
Iterations

Useful iterations: done (1.2s)

IterNodesCost
034220889
183017353
2303312190
done500111553

prune2.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 14.9b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02665
13451
done3451

end0.0ms

sample224.0ms

Algorithm
intervals
Results
134.0ms8000×body80valid