Details

sample565.0ms

Algorithm: halfpoints

simplify4.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	3108
7	1340
6	477
5	194
4	121
3	79
2	48
1	30
0	16

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.5b

localize95.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
56.6b	(- (exp x) (exp (- x)))

rewrite175.0ms

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` `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 → 122

Calls

4 calls:

20.0ms	(+ (exp x) (exp (- x)))
65.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
51.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
34.0ms	(- (exp x) (exp (- x)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (exp x) (exp (- x)))
76.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
119.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.0ms	(- (exp x) (exp (- x)))

simplify2.0s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
2	1904
1	582
0	231

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize130.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
33×	`associate-l`
30×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`times-frac`
21×	`add-cbrt-cube` `add-exp-log`
15×	`pow1`
12×	`associate-r`
8×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 116

Calls

4 calls:

12.0ms	(* x (+ 2 (* (* x x) 1/3)))
59.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
27.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* (* x x) 1/3)))) 2.0) (sin y))
28.0ms	(* (* x x) 1/3)

series450.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* x (+ 2 (* (* x x) 1/3)))
102.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
155.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* (* x x) 1/3)))) 2.0) (sin y))
46.0ms	(* (* x x) 1/3)

simplify2.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	5002
2	2208
1	647
0	238

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize127.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) 1/3)
0.2b	(* (* x x) 1/3)
0.4b	(* (* x (sqrt (+ 2 (* (* x x) 1/3)))) (sqrt (+ 2 (* (* x x) 1/3))))
0.4b	(* x (sqrt (+ 2 (* (* x x) 1/3))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`associate-r`
17×	`add-sqr-sqrt`
14×	`sqrt-div`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
7×	`flip3-+` `sqrt-prod` `flip-+`
6×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `*-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`

Counts

4 → 99

Calls

4 calls:

18.0ms	(* (* x x) 1/3)
26.0ms	(* (* x x) 1/3)
61.0ms	(* (* x (sqrt (+ 2 (* (* x x) 1/3)))) (sqrt (+ 2 (* (* x x) 1/3))))
39.0ms	(* x (sqrt (+ 2 (* (* x x) 1/3))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* x x) 1/3)
49.0ms	(* (* x x) 1/3)
155.0ms	(* (* x (sqrt (+ 2 (* (* x x) 1/3)))) (sqrt (+ 2 (* (* x x) 1/3))))
174.0ms	(* x (sqrt (+ 2 (* (* x x) 1/3))))

simplify1.8s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	1490
1	419
0	147

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

localize146.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) 1/3)
0.2b	(* (* x x) 1/3)
0.3b	(* (* x (sqrt (+ 2 (* (* x x) 1/3)))) (* (cbrt (sqrt (+ 2 (* (* x x) 1/3)))) (cbrt (sqrt (+ 2 (* (* x x) 1/3))))))
0.4b	(* x (sqrt (+ 2 (* (* x x) 1/3))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

56×	`sqrt-div`
36×	`cbrt-div`
34×	`associate-*r/`
28×	`frac-times` `pow1` `flip3-+` `add-exp-log` `flip-+`
24×	`add-cbrt-cube`
15×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-*l/`
6×	`associate-l`
4×	`expm1-log1p-u` `*-commutative` `sqrt-prod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

21.0ms	(* (* x x) 1/3)
16.0ms	(* (* x x) 1/3)
101.0ms	(* (* x (sqrt (+ 2 (* (* x x) 1/3)))) (* (cbrt (sqrt (+ 2 (* (* x x) 1/3)))) (cbrt (sqrt (+ 2 (* (* x x) 1/3))))))
21.0ms	(* x (sqrt (+ 2 (* (* x x) 1/3))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* x x) 1/3)
55.0ms	(* (* x x) 1/3)
346.0ms	(* (* x (sqrt (+ 2 (* (* x x) 1/3)))) (* (cbrt (sqrt (+ 2 (* (* x x) 1/3)))) (cbrt (sqrt (+ 2 (* (* x x) 1/3))))))
220.0ms	(* x (sqrt (+ 2 (* (* x x) 1/3))))

simplify2.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	2207
1	675
0	234

prune1.7s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.0b

regimes364.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample13.5s

Algorithm: halfpoints