Details

sample4.2s

Algorithm: halfpoints

simplify22.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
8	2530
7	1175
6	432
5	178
4	111
3	79
2	48
1	30
0	16

prune85.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.2b

localize246.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.0b	(- (exp x) (exp (- x)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
23×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 99

Calls

4 calls:

223.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
342.0ms	(+ (exp x) (exp (- x)))
141.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
665.0ms	(- (exp x) (exp (- x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

364.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
68.0ms	(+ (exp x) (exp (- x)))
600.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
288.0ms	(- (exp x) (exp (- x)))

simplify10.2s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	1796
1	524
0	200

prune2.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize441.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.1b	(* 1/60 (pow x 5))
0.1b	(* (/ (+ (* x (+ (* (* x x) 1/3) 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
0.2b	(* (* x x) 1/3)

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`add-exp-log`
18×	`*-un-lft-identity`
17×	`associate-l`
16×	`add-cube-cbrt` `add-cbrt-cube`
13×	`associate-r`
11×	`pow1`
10×	`times-frac`
8×	`prod-exp`
6×	`cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down`
3×	`*-commutative`
2×	`sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `flip3-+` `div-exp` `associate-*l/` `pow-exp` `sum-log` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 88

Calls

4 calls:

94.0ms	(+ (exp x) (exp (- x)))
62.0ms	(* 1/60 (pow x 5))
387.0ms	(* (/ (+ (* x (+ (* (* x x) 1/3) 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
43.0ms	(* (* x x) 1/3)

series1.1s

Counts

4 → 12

Calls

4 calls:

115.0ms	(+ (exp x) (exp (- x)))
416.0ms	(* 1/60 (pow x 5))
452.0ms	(* (/ (+ (* x (+ (* (* x x) 1/3) 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
115.0ms	(* (* x x) 1/3)

simplify6.7s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	1591
1	498
0	197

prune3.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize397.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y)))
0.3b	(* (/ 1 (sqrt 2.0)) (/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y))))
0.4b	(/ (sqrt 2.0) (sin y))
1.0b	(/ 1 (sqrt 2.0))

rewrite25.4s

Algorithm

rewrite-expression-head

Rules

513×	`times-frac`
469×	`*-un-lft-identity`
309×	`add-sqr-sqrt`
236×	`add-cube-cbrt`
145×	`sqrt-prod`
135×	`distribute-lft-out`
115×	`associate-r`
54×	`add-exp-log`
34×	`add-cbrt-cube`
31×	`associate-/r*`
24×	`div-exp`
22×	`associate-l`
20×	`unswap-sqr`
16×	`div-inv`
14×	`cbrt-undiv` `associate-/l*`
12×	`prod-exp`
8×	`pow1`
6×	`cbrt-unprod` `associate-/l/`
5×	`flip3-+` `flip-+`
4×	`rec-exp` `1-exp` `frac-add` `add-log-exp`
3×	`pow-flip` `frac-2neg` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 429

Calls

4 calls:

10.2s	(/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y)))
14.8s	(* (/ 1 (sqrt 2.0)) (/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y))))
40.0ms	(/ (sqrt 2.0) (sin y))
11.0ms	(/ 1 (sqrt 2.0))

series1.4s

Counts

4 → 10

Calls

4 calls:

465.0ms	(/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y)))
842.0ms	(* (/ 1 (sqrt 2.0)) (/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y))))
139.0ms	(/ (sqrt 2.0) (sin y))
0.0ms	(/ 1 (sqrt 2.0))

simplify16.5s

Counts

439 → 439

Iterations

Iter	Nodes
done	5000
2	4944
1	1486
0	456

prune11.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize667.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y))))
0.4b	(/ (sqrt 2.0) (sin y))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite14.0s

Algorithm

rewrite-expression-head

Rules

1587×	`times-frac`
1352×	`sqrt-prod`
1095×	`add-sqr-sqrt`
826×	`*-un-lft-identity`
680×	`add-cube-cbrt`
283×	`associate-l`
115×	`associate-r`
92×	`unswap-sqr`
79×	`add-exp-log`
66×	`distribute-lft-out`
49×	`add-cbrt-cube`
42×	`div-exp`
40×	`associate-/l*`
33×	`div-inv`
23×	`cbrt-undiv`
21×	`associate-/r*`
20×	`pow1` `sqrt-pow1`
15×	`prod-exp`
14×	`pow-flip`
10×	`pow1/2` `pow-div`
9×	`cbrt-unprod`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`inv-pow`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `*-commutative` `associate-/l/`

Counts

4 → 970

Calls

4 calls:

13.0s	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y))))
23.0ms	(/ (sqrt 2.0) (sin y))
329.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
19.0ms	(/ 1 (sqrt (sqrt 2.0)))

series819.0ms

Counts

4 → 8

Calls

4 calls:

711.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (/ (+ (+ (* (* (* x (* x x)) (* x x)) 1/60) (* (* (* x x) x) 1/3)) (+ x x)) (/ (sqrt 2.0) (sin y))))
108.0ms	(/ (sqrt 2.0) (sin y))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify9.7s

Counts

978 → 978

Iterations

Iter	Nodes
done	5000
1	2335
0	747

prune22.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes516.0ms

Accuracy

44.2% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.7b

bsearch410.0ms

Steps

Iters	Range		Point
9	-1.0033578155902432	-1.1785608538762668e-07	-0.011756186125805182

simplify19.0ms

Iterations

Iter	Nodes
done	48
1	48
0	37

end0.0ms

sample48.0s

Algorithm: halfpoints