Details

sample801.0ms

Algorithm: halfpoints

simplify4.6s

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.8b

localize70.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
59.8b	(- (exp x) (exp (- x)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`associate-l`
16×	`times-frac`
9×	`prod-diff`
8×	`add-cbrt-cube` `add-exp-log`
7×	`add-log-exp`
5×	`pow1`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `fma-def` `fma-neg` `associate-r` `log1p-expm1-u`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv` `flip--` `distribute-lft-out`

Counts

3 → 85

Calls

3 calls:

15.0ms	(+ (exp x) (exp (- x)))
53.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
13.0ms	(- (exp x) (exp (- x)))

series220.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (exp x) (exp (- x)))
126.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
55.0ms	(- (exp x) (exp (- x)))

simplify3.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	4390
2	1272
1	419
0	169

prune824.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize102.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`associate-l`
16×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
13×	`pow1`
10×	`times-frac`
9×	`associate-r`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `sum-log` `distribute-lft-in` `div-exp` `associate-*l/` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

10.0ms	(+ (exp x) (exp (- x)))
63.0ms	(* x (+ (* (* x x) 1/3) 2))
15.0ms	(* (/ (fma 1/60 (pow x 5) (* x (+ (* (* x x) 1/3) 2))) 2.0) (sin y))
26.0ms	(* (* x x) 1/3)

series325.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (exp x) (exp (- x)))
111.0ms	(* x (+ (* (* x x) 1/3) 2))
135.0ms	(* (/ (fma 1/60 (pow x 5) (* x (+ (* (* x x) 1/3) 2))) 2.0) (sin y))
39.0ms	(* (* x x) 1/3)

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
2	2066
1	550
0	198

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/12 (* (* x x) (* x x)) (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(* (/ (fma 1/60 (pow x 5) (* x (+ (* (* x x) 1/3) 2))) 2.0) (sin y))
0.2b	(* (* x x) 1/3)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
36×	`pow-prod-up`
27×	`pow-prod-down`
26×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
19×	`add-sqr-sqrt`
18×	`pow-plus`
15×	`associate-l`
13×	`pow2` `*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
10×	`times-frac`
7×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
1×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 130

Calls

4 calls:

0.0ms	(fma 1/12 (* (* x x) (* x x)) (* x x))
29.0ms	(* (* x x) (* x x))
14.0ms	(* (/ (fma 1/60 (pow x 5) (* x (+ (* (* x x) 1/3) 2))) 2.0) (sin y))
17.0ms	(* (* x x) 1/3)

series380.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(fma 1/12 (* (* x x) (* x x)) (* x x))
60.0ms	(* (* x x) (* x x))
133.0ms	(* (/ (fma 1/60 (pow x 5) (* x (+ (* (* x x) 1/3) 2))) 2.0) (sin y))
41.0ms	(* (* x x) 1/3)

simplify3.5s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
3	4554
2	1291
1	449
0	172

prune973.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize107.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) 1/3)
0.2b	(* (* x x) 1/3)
0.4b	(* x (sqrt (+ (* (* x x) 1/3) 2)))
0.5b	(* (* x (sqrt (+ (* (* x x) 1/3) 2))) (sqrt (+ (* (* x x) 1/3) 2)))

rewrite233.0ms

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:

15.0ms	(* (* x x) 1/3)
16.0ms	(* (* x x) 1/3)
56.0ms	(* x (sqrt (+ (* (* x x) 1/3) 2)))
143.0ms	(* (* x (sqrt (+ (* (* x x) 1/3) 2))) (sqrt (+ (* (* x x) 1/3) 2)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* x x) 1/3)
42.0ms	(* (* x x) 1/3)
150.0ms	(* x (sqrt (+ (* (* x x) 1/3) 2)))
114.0ms	(* (* x (sqrt (+ (* (* x x) 1/3) 2))) (sqrt (+ (* (* x x) 1/3) 2)))

simplify1.9s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	1480
1	423
0	147

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes299.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample12.2s

Algorithm: halfpoints