Details

Time bar (total: 30.9s)

sample300.0ms

Algorithm
halfpoints

simplify13.8s

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01624
13011
24611
38311
412611
520311
636511
769311
8117711
9370311
done500011

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize35.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.7b
(- (exp x) (exp (- x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
27×*-un-lft-identity
19×add-cube-cbrt associate-*l*
16×times-frac
9×prod-diff
7×add-exp-log add-cbrt-cube
4×pow1 distribute-lft-out-- add-log-exp difference-of-squares
3×fma-neg associate-*r*
2×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u unswap-sqr
1×cbrt-undiv sub-neg flip3-- diff-log div-exp pow-prod-down associate-*l/ *-commutative flip-- div-inv
Counts
2 → 68
Calls
2 calls:
26.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
7.0ms
(- (exp x) (exp (- x)))

series117.0ms

Counts
2 → 6
Calls
2 calls:
79.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
38.0ms
(- (exp x) (exp (- x)))

simplify2.6s

Counts
74 → 74
Iterations

Useful iterations: 3 (705.0ms)

IterNodesCost
01491156
13491004
2960843
34547815
done5000815

prune196.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1/60 (pow x 5) (* 2 x))
0.0b
(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
0.1b
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
13×associate-*l*
11×add-cube-cbrt *-un-lft-identity
10×times-frac
8×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
2×prod-exp cbrt-unprod fma-udef unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
3 → 54
Calls
3 calls:
0.0ms
(fma 1/60 (pow x 5) (* 2 x))
0.0ms
(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
8.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series266.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(fma 1/60 (pow x 5) (* 2 x))
58.0ms
(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
88.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify1.2s

Counts
63 → 63
Iterations

Useful iterations: 3 (387.0ms)

IterNodesCost
01091189
12311173
27491017
332111015
done50001015

prune226.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.3b
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b
(/ 1 (sqrt 2.0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
69×add-sqr-sqrt
61×add-cube-cbrt *-un-lft-identity
54×add-exp-log
44×associate-*l*
43×sqrt-prod
34×add-cbrt-cube
22×prod-exp
14×div-exp
13×pow1
12×associate-/r* cbrt-unprod
8×cbrt-undiv
6×associate-/l*
4×expm1-log1p-u rec-exp 1-exp associate-*r* pow-prod-down associate-*l/ log1p-expm1-u div-inv add-log-exp
3×pow-flip unswap-sqr
2×frac-2neg clear-num *-commutative
1×frac-times sqrt-pow1 pow1/2 associate-*r/ inv-pow
Counts
4 → 188
Calls
4 calls:
12.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
25.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
3.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
3.0ms
(/ 1 (sqrt 2.0))

series486.0ms

Counts
4 → 10
Calls
4 calls:
156.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
211.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
118.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify758.0ms

Counts
198 → 198
Iterations

Useful iterations: 2 (287.0ms)

IterNodesCost
02544584
16344231
220423579
done50003579

prune581.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
1128×sqrt-prod
1116×times-frac
592×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
283×associate-*l*
79×add-exp-log
49×add-cbrt-cube
37×associate-/l*
32×div-exp
25×prod-exp
24×associate-/r*
23×pow1 div-inv
20×sqrt-pow1
17×cbrt-undiv
15×cbrt-unprod
14×pow-flip
10×pow1/2 pow-div
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg pow-prod-down associate-*l/ clear-num
2×inv-pow
1×frac-times associate-*r/ associate-*r* *-commutative associate-/l/
Counts
4 → 773
Calls
4 calls:
107.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
3.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
17.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
4.0ms
(/ 1 (sqrt (sqrt 2.0)))

series337.0ms

Counts
4 → 8
Calls
4 calls:
219.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
118.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify1.6s

Counts
781 → 781
Iterations

Useful iterations: done (1.5s)

IterNodesCost
061420031
1168517143
2406015363
done500115081

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes84.0ms

Accuracy

48.4% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.8b

bsearch101.0ms

Steps
ItersRangePoint
8
-0.48869560230416215
-0.0008391074150366579
-0.015295351353249335

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02633
13033
done3033

end0.0ms

sample6.0s

Algorithm
halfpoints