Details

sample488.0ms

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.7b

localize100.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.2b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.3b	(- (exp x) (exp (- x)))

rewrite161.0ms

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:

68.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
10.0ms	(+ (exp x) (exp (- x)))
62.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
12.0ms	(- (exp x) (exp (- x)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
27.0ms	(+ (exp x) (exp (- x)))
107.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
67.0ms	(- (exp x) (exp (- x)))

simplify2.2s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	1905
1	581
0	231

prune927.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize108.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

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)))
12.0ms	(* x (+ 2 (* (* x x) 1/3)))
22.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* (* x x) 1/3)))) 2.0) (sin y))
25.0ms	(* (* x x) 1/3)

series371.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (exp x) (exp (- x)))
136.0ms	(* x (+ 2 (* (* x x) 1/3)))
145.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* (* x x) 1/3)))) 2.0) (sin y))
45.0ms	(* (* x x) 1/3)

simplify1.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5009
2	2043
1	549
0	198

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize164.0ms

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

rewrite484.0ms

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:

17.0ms	(* (* x x) 1/3)
408.0ms	(* (* x x) 1/3)
40.0ms	(* (* x (sqrt (+ 2 (* (* x x) 1/3)))) (sqrt (+ 2 (* (* x x) 1/3))))
15.0ms	(* x (sqrt (+ 2 (* (* x x) 1/3))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* x x) 1/3)
34.0ms	(* (* x x) 1/3)
117.0ms	(* (* x (sqrt (+ 2 (* (* x x) 1/3)))) (sqrt (+ 2 (* (* x x) 1/3))))
137.0ms	(* x (sqrt (+ 2 (* (* x x) 1/3))))

simplify2.0s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	1490
1	419
0	147

prune956.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize137.0ms

Local error

Found 4 expressions with local error:

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

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-cbrt-cube` `add-exp-log`
26×	`sqrt-div`
19×	`pow1`
16×	`associate-*r/`
14×	`add-sqr-sqrt`
12×	`-un-lft-identity` `associate-r*` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
9×	`pow-prod-down` `sqrt-prod`
8×	`frac-times` `associate-/l/`
7×	`flip3--` `flip--`
6×	`associate-/r*` `flip3-+` `times-frac` `flip-+`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `*-commutative`
2×	`associate-/r/` `unswap-sqr`
1×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 114

Calls

4 calls:

28.0ms	(* (* x x) 1/3)
17.0ms	(* (* x x) 1/3)
74.0ms	(/ (* (* x (sqrt (- (* 2 2) (* (* (* x x) 1/3) (* (* x x) 1/3))))) (sqrt (+ 2 (* (* x x) 1/3)))) (sqrt (- 2 (* (* x x) 1/3))))
89.0ms	(* (* x (sqrt (- (* 2 2) (* (* (* x x) 1/3) (* (* x x) 1/3))))) (sqrt (+ 2 (* (* x x) 1/3))))

series773.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* x x) 1/3)
35.0ms	(* (* x x) 1/3)
420.0ms	(/ (* (* x (sqrt (- (* 2 2) (* (* (* x x) 1/3) (* (* x x) 1/3))))) (sqrt (+ 2 (* (* x x) 1/3)))) (sqrt (- 2 (* (* x x) 1/3))))
273.0ms	(* (* x (sqrt (- (* 2 2) (* (* (* x x) 1/3) (* (* x x) 1/3))))) (sqrt (+ 2 (* (* x x) 1/3))))

simplify2.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	2239
1	601
0	217

prune1.5s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes267.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample12.4s

Algorithm: halfpoints