Details

sample444.0ms

Algorithm: halfpoints

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2148
8	2148
7	1410
6	468
5	192
4	123
3	80
2	48
1	30
0	16

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
57.5b	(- (exp x) (exp (- x)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
35×	`associate-l`
31×	`add-cube-cbrt`
29×	`times-frac`
14×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`fma-def` `fma-neg`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 126

Calls

4 calls:

10.0ms	(+ (exp x) (exp (- x)))
38.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
43.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
12.0ms	(- (exp x) (exp (- x)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (exp x) (exp (- x)))
71.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
102.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
49.0ms	(- (exp x) (exp (- x)))

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	2000
3	2000
2	1872
1	582
0	232

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize148.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) 1/3)
0.2b	(* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) 2) (sin y))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt`
15×	`associate-l`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`prod-exp` `cbrt-unprod`
10×	`times-frac` `pow-prod-down`
9×	`associate-r`
6×	`pow-plus` `pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `unswap-sqr`
2×	`pow2` `pow-sqr`
1×	`cbrt-undiv` `div-exp` `pow3` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))
17.0ms	(* (* x x) x)
52.0ms	(* (* (* x x) x) 1/3)
26.0ms	(* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) 2) (sin y))

series400.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))
45.0ms	(* (* x x) x)
49.0ms	(* (* (* x x) x) 1/3)
111.0ms	(* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) 2) (sin y))

simplify1.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	2001
3	2001
2	1013
1	353
0	158

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize126.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
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/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-*r/` `inv-pow`

Counts

4 → 192

Calls

4 calls:

15.0ms	(* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2)) (sin y))
57.0ms	(* (/ 1 (sqrt 2)) (* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2)) (sin y)))
10.0ms	(/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2))
10.0ms	(/ 1 (sqrt 2))

series614.0ms

Counts

4 → 10

Calls

4 calls:

220.0ms	(* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2)) (sin y))
246.0ms	(* (/ 1 (sqrt 2)) (* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2)) (sin y)))
145.0ms	(/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2))
0.0ms	(/ 1 (sqrt 2))

simplify1.3s

Counts

202 → 202

Iterations

Iter	Nodes
done	2004
3	2004
2	1853
1	649
0	257

prune4.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize120.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

1128×	`sqrt-prod`
1116×	`times-frac`
592×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*l/`
2×	`inv-pow`
1×	`frac-times` `associate-r` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 777

Calls

4 calls:

64.0ms	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2)) (sin y)))
5.0ms	(/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2))
6.0ms	(/ 1 (sqrt (sqrt 2)))
12.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series446.0ms

Counts

4 → 8

Calls

4 calls:

288.0ms	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2)) (sin y)))
158.0ms	(/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2))
0.0ms	(/ 1 (sqrt (sqrt 2)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify1.8s

Counts

785 → 785

Iterations

Iter	Nodes
done	2002
2	2002
1	1721
0	617

prune20.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes283.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample11.8s

Algorithm: halfpoints