Details

sample409.0ms

Algorithm: halfpoints

simplify1.2s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.5b

localize107.0ms

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))
58.4b	(- (exp x) (exp (- x)))

rewrite171.0ms

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:

19.0ms	(+ (exp x) (exp (- x)))
56.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
58.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
31.0ms	(- (exp x) (exp (- x)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (exp x) (exp (- x)))
89.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
95.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
70.0ms	(- (exp x) (exp (- x)))

simplify2.0s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	2816
1	583
0	231

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize98.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* x x) (* x 1/3) (* 2 x))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b	(* (/ (fma (pow x 5) 1/60 (fma (* x x) (* x 1/3) (* 2 x))) 2.0) (sin y))
0.4b	(* x 1/3)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma (* x x) (* x 1/3) (* 2 x))
57.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
27.0ms	(* (/ (fma (pow x 5) 1/60 (fma (* x x) (* x 1/3) (* 2 x))) 2.0) (sin y))
10.0ms	(* x 1/3)

series395.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(fma (* x x) (* x 1/3) (* 2 x))
105.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
142.0ms	(* (/ (fma (pow x 5) 1/60 (fma (* x x) (* x 1/3) (* 2 x))) 2.0) (sin y))
27.0ms	(* x 1/3)

simplify1.6s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	2229
1	493
0	208

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize134.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b	(/ 2.0 (sin y))
0.2b	(/ (fma 1/60 (pow x 5) (* x (fma (* 1/3 x) x 2))) (/ 2.0 (sin y)))
0.4b	(* 1/3 x)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
72×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
65×	`add-cube-cbrt`
19×	`associate-l`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
8×	`pow1`
7×	`div-inv`
6×	`associate-r` `associate-/l*`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative`
1×	`associate-*l/` `associate-/r/`

Counts

4 → 158

Calls

4 calls:

59.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
8.0ms	(/ 2.0 (sin y))
22.0ms	(/ (fma 1/60 (pow x 5) (* x (fma (* 1/3 x) x 2))) (/ 2.0 (sin y)))
10.0ms	(* 1/3 x)

series276.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
33.0ms	(/ 2.0 (sin y))
140.0ms	(/ (fma 1/60 (pow x 5) (* x (fma (* 1/3 x) x 2))) (/ 2.0 (sin y)))
26.0ms	(* 1/3 x)

simplify1.9s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	3633
1	726
0	296

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize165.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 5) 1/60)
0.3b	(/ (/ (fma (fma 1/3 (* x x) 2) x (* (pow x 5) 1/60)) (sqrt 2.0)) (/ (sqrt 2.0) (sin y)))
0.5b	(/ (sqrt 2.0) (sin y))
0.5b	(/ (fma (fma 1/3 (* x x) 2) x (* (pow x 5) 1/60)) (sqrt 2.0))

rewrite501.0ms

Algorithm

rewrite-expression-head

Rules

1348×	`times-frac`
640×	`add-sqr-sqrt`
635×	`*-un-lft-identity` `add-cube-cbrt`
438×	`sqrt-prod`
49×	`div-inv`
31×	`associate-/r` `associate-/l`
25×	`add-exp-log`
22×	`add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
7×	`associate-l`
4×	`expm1-log1p-u` `pow1` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `prod-exp` `unswap-sqr`
2×	`sqr-pow`
1×	`pow-to-exp` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 659

Calls

4 calls:

10.0ms	(* (pow x 5) 1/60)
50.0ms	(/ (/ (fma (fma 1/3 (* x x) 2) x (* (pow x 5) 1/60)) (sqrt 2.0)) (/ (sqrt 2.0) (sin y)))
12.0ms	(/ (sqrt 2.0) (sin y))
10.0ms	(/ (fma (fma 1/3 (* x x) 2) x (* (pow x 5) 1/60)) (sqrt 2.0))

series571.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (pow x 5) 1/60)
254.0ms	(/ (/ (fma (fma 1/3 (* x x) 2) x (* (pow x 5) 1/60)) (sqrt 2.0)) (/ (sqrt 2.0) (sin y)))
72.0ms	(/ (sqrt 2.0) (sin y))
174.0ms	(/ (fma (fma 1/3 (* x x) 2) x (* (pow x 5) 1/60)) (sqrt 2.0))

simplify2.6s

Counts

671 → 671

Iterations

Iter	Nodes
done	5002
1	3031
0	842

prune5.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes206.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample13.3s

Algorithm: halfpoints