Details

sample433.0ms

Algorithm: halfpoints

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1025
5	247
4	128
3	83
2	48
1	30
0	16

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 46.5b

localize77.0ms

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))
58.8b	(- (exp x) (exp (- x)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
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:

43.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
43.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.0ms	(- (exp x) (exp (- x)))

series231.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
118.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
40.0ms	(- (exp x) (exp (- x)))

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2572
1	547
0	217

prune763.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`associate-l`
28×	`*-un-lft-identity`
23×	`times-frac`
22×	`add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`pow1`
7×	`associate-r` `prod-exp` `cbrt-unprod`
5×	`pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `div-inv`
1×	`fma-udef`

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma 1/60 (pow x 5) (fma (* 1/3 (* x x)) x (* x 2)))
65.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
23.0ms	(* (/ (fma 1/60 (pow x 5) (fma (* 1/3 (* x x)) x (* x 2))) 2.0) (sin y))
18.0ms	(* 1/3 (* x x))

series338.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma 1/60 (pow x 5) (fma (* 1/3 (* x x)) x (* x 2)))
91.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
144.0ms	(* (/ (fma 1/60 (pow x 5) (fma (* 1/3 (* x x)) x (* x 2))) 2.0) (sin y))
39.0ms	(* 1/3 (* x x))

simplify1.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	2694
1	515
0	207

prune988.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize129.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
62×	`add-sqr-sqrt`
57×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*` `add-exp-log`
13×	`add-cbrt-cube`
7×	`associate-r`
6×	`div-inv` `associate-/l*`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `unpow-prod-down` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `prod-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 138

Calls

4 calls:

0.0ms	(fma x (fma 1/3 (* x x) 2) (* 1/60 (pow x 5)))
9.0ms	(* 1/60 (pow x 5))
4.0ms	(/ 2.0 (sin y))
8.0ms	(/ (fma x (fma 1/3 (* x x) 2) (* 1/60 (pow x 5))) (/ 2.0 (sin y)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(fma x (fma 1/3 (* x x) 2) (* 1/60 (pow x 5)))
66.0ms	(* 1/60 (pow x 5))
25.0ms	(/ 2.0 (sin y))
124.0ms	(/ (fma x (fma 1/3 (* x x) 2) (* 1/60 (pow x 5))) (/ 2.0 (sin y)))

simplify1.6s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2834
1	580
0	244

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize160.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/60 (pow x 5))
0.2b	(/ (fma x (fma 1/3 (* x x) 2) (* 1/60 (pow x 5))) (* (sqrt 2.0) (/ (sqrt 2.0) (sin y))))
0.4b	(* (sqrt 2.0) (/ (sqrt 2.0) (sin y)))
0.5b	(/ (sqrt 2.0) (sin y))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
43×	`times-frac`
39×	`*-un-lft-identity` `add-cube-cbrt`
29×	`associate-r` `sqrt-prod`
25×	`add-exp-log`
22×	`add-cbrt-cube`
9×	`associate-l` `associate-/l*` `unswap-sqr`
7×	`prod-exp`
6×	`pow1` `cbrt-undiv` `div-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-r/` `-commutative` `sqr-pow`
1×	`pow-to-exp` `pow-prod-down` `pow-exp` `associate-/r/`

Counts

4 → 144

Calls

4 calls:

9.0ms	(* 1/60 (pow x 5))
17.0ms	(/ (fma x (fma 1/3 (* x x) 2) (* 1/60 (pow x 5))) (* (sqrt 2.0) (/ (sqrt 2.0) (sin y))))
29.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (sin y)))
6.0ms	(/ (sqrt 2.0) (sin y))

series548.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* 1/60 (pow x 5))
282.0ms	(/ (fma x (fma 1/3 (* x x) 2) (* 1/60 (pow x 5))) (* (sqrt 2.0) (/ (sqrt 2.0) (sin y))))
110.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (sin y)))
63.0ms	(/ (sqrt 2.0) (sin y))

simplify4.3s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	3880
1	559
0	235

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes223.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample12.5s

Algorithm: halfpoints