Details

Time bar (total: 40.1s)

sample571.0ms

Algorithm
halfpoints

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
01624
13011
24811
38311
412811
524711
6103711
done500111

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 47.9b

localize111.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.9b
(- (exp x) (exp (- x)))

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
43×*-un-lft-identity
35×associate-*l*
29×add-cube-cbrt times-frac
13×add-exp-log add-cbrt-cube
9×prod-diff
7×pow1
6×associate-*r*
5×add-log-exp
4×prod-exp cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
3×expm1-log1p-u fma-neg log1p-expm1-u distribute-lft-out
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 105
Calls
3 calls:
99.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
104.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
41.0ms
(- (exp x) (exp (- x)))

series308.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
136.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
69.0ms
(- (exp x) (exp (- x)))

simplify2.6s

Counts
114 → 114
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02181732
15581576
227281352
done50001294

prune929.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize134.0ms

Local error

Found 4 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)))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
29×associate-*l*
27×*-un-lft-identity
23×times-frac
21×add-cube-cbrt
14×add-exp-log add-cbrt-cube
8×pow1
6×associate-*r*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×distribute-lft-out
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative fma-udef div-inv
Counts
4 → 91
Calls
4 calls:
0.0ms
(fma 1/60 (pow x 5) (* 2 x))
1.0ms
(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
105.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
31.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series601.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(fma 1/60 (pow x 5) (* 2 x))
101.0ms
(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
102.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
148.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify2.0s

Counts
103 → 103
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01861765
14531744
222421526
done50021516

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize164.0ms

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))
0.4b
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b
(/ 1 (sqrt 2.0))

rewrite206.0ms

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:
49.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
117.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
11.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
13.0ms
(/ 1 (sqrt 2.0))

series846.0ms

Counts
4 → 10
Calls
4 calls:
261.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
365.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
218.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify4.7s

Counts
198 → 198
Iterations

Useful iterations: done (4.7s)

IterNodesCost
02544584
16644327
238823773
done50013735

prune2.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize180.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sin y) (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b
(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (sin y) (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.5b
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b
(/ (sqrt 1) (sqrt (sqrt 2.0)))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
228×sqrt-prod
153×times-frac
133×add-sqr-sqrt
110×*-un-lft-identity
107×add-cube-cbrt
58×associate-*l*
49×add-exp-log add-cbrt-cube
24×associate-/r*
18×cbrt-undiv div-exp
14×prod-exp cbrt-unprod
13×associate-*r*
10×associate-/l* unswap-sqr
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-*r/
1×frac-times sqrt-undiv pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 274
Calls
4 calls:
37.0ms
(/ (* (sin y) (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0)))
168.0ms
(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (sin y) (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0))))
16.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
18.0ms
(/ (sqrt 1) (sqrt (sqrt 2.0)))

series1.5s

Counts
4 → 10
Calls
4 calls:
769.0ms
(/ (* (sin y) (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0)))
560.0ms
(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (sin y) (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0))))
215.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms
(/ (sqrt 1) (sqrt (sqrt 2.0)))

simplify780.0ms

Counts
284 → 284
Iterations

Useful iterations: done (757.0ms)

IterNodesCost
03427949
19087089
done50016221

prune3.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes308.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02531
12931
done2931

end0.0ms

sample15.0s

Algorithm
halfpoints