Details

sample2.1s

Algorithm: halfpoints

simplify11.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	3100
7	1354
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: 45.2b

localize106.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.0b	(- (exp x) (exp (- x)))

rewrite393.0ms

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-exp-log` `add-cbrt-cube`
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` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 122

Calls

4 calls:

157.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
27.0ms	(+ (exp x) (exp (- x)))
147.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
52.0ms	(- (exp x) (exp (- x)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
43.0ms	(+ (exp x) (exp (- x)))
150.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
65.0ms	(- (exp x) (exp (- x)))

simplify4.5s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	1871
1	589
0	232

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize165.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`associate-l`
18×	`*-un-lft-identity`
16×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
13×	`pow1`
10×	`times-frac`
7×	`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×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-*l/` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

59.0ms	(* x (+ 2 (* 1/3 (* x x))))
21.0ms	(+ (exp x) (exp (- x)))
52.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* 1/3 (* x x))))) 2.0) (sin y))
35.0ms	(* 1/3 (* x x))

series415.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* x (+ 2 (* 1/3 (* x x))))
46.0ms	(+ (exp x) (exp (- x)))
161.0ms	(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* 1/3 (* x x))))) 2.0) (sin y))
48.0ms	(* 1/3 (* x x))

simplify5.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5004
2	2045
1	547
0	197

prune1.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize168.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt 2.0) (sin y)))
0.3b	(* (/ 1 (sqrt 2.0)) (/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt 2.0) (sin y))))
0.4b	(/ (sqrt 2.0) (sin y))
1.0b	(/ 1 (sqrt 2.0))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

353×	`times-frac`
257×	`add-sqr-sqrt`
192×	`*-un-lft-identity`
184×	`add-cube-cbrt`
109×	`sqrt-prod`
71×	`associate-r`
54×	`add-exp-log`
34×	`add-cbrt-cube`
31×	`associate-/r*`
24×	`div-exp`
22×	`associate-l`
20×	`unswap-sqr`
14×	`cbrt-undiv`
12×	`prod-exp` `div-inv` `associate-/l*`
8×	`pow1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `frac-2neg` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 341

Calls

4 calls:

27.0ms	(/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt 2.0) (sin y)))
140.0ms	(* (/ 1 (sqrt 2.0)) (/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt 2.0) (sin y))))
43.0ms	(/ (sqrt 2.0) (sin y))
14.0ms	(/ 1 (sqrt 2.0))

series2.0s

Counts

4 → 10

Calls

4 calls:

767.0ms	(/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt 2.0) (sin y)))
907.0ms	(* (/ 1 (sqrt 2.0)) (/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt 2.0) (sin y))))
304.0ms	(/ (sqrt 2.0) (sin y))
0.0ms	(/ 1 (sqrt 2.0))

simplify9.1s

Counts

351 → 351

Iterations

Iter	Nodes
done	5002
2	3930
1	1337
0	434

prune8.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

localize213.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ 1 (sqrt 2.0)) (sqrt (sqrt 2.0))) (/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt (sqrt 2.0)) (sin y))))
0.3b	(/ (sqrt (sqrt 2.0)) (sin y))
1.0b	(/ 1 (sqrt 2.0))
1.0b	(/ (/ 1 (sqrt 2.0)) (sqrt (sqrt 2.0)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1204×	`times-frac`
890×	`add-sqr-sqrt`
858×	`sqrt-prod`
543×	`*-un-lft-identity`
513×	`add-cube-cbrt`
202×	`associate-l`
98×	`associate-r`
80×	`unswap-sqr`
79×	`add-exp-log`
49×	`add-cbrt-cube`
42×	`div-exp`
34×	`associate-/l*`
27×	`div-inv`
23×	`cbrt-undiv`
18×	`associate-/r*`
16×	`pow1`
15×	`prod-exp`
11×	`sqrt-pow1`
9×	`pow-flip` `cbrt-unprod`
8×	`pow-div`
7×	`pow1/2`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `inv-pow`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `*-commutative` `associate-/l/`

Counts

4 → 774

Calls

4 calls:

856.0ms	(* (/ (/ 1 (sqrt 2.0)) (sqrt (sqrt 2.0))) (/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt (sqrt 2.0)) (sin y))))
20.0ms	(/ (sqrt (sqrt 2.0)) (sin y))
15.0ms	(/ 1 (sqrt 2.0))
47.0ms	(/ (/ 1 (sqrt 2.0)) (sqrt (sqrt 2.0)))

series1.6s

Counts

4 → 8

Calls

4 calls:

1.0s	(* (/ (/ 1 (sqrt 2.0)) (sqrt (sqrt 2.0))) (/ (fma 1/60 (pow x 5) (* x (fma (* x x) 1/3 2))) (/ (sqrt (sqrt 2.0)) (sin y))))
542.0ms	(/ (sqrt (sqrt 2.0)) (sin y))
0.0ms	(/ 1 (sqrt 2.0))
0.0ms	(/ (/ 1 (sqrt 2.0)) (sqrt (sqrt 2.0)))

simplify8.9s

Counts

782 → 782

Iterations

Iter	Nodes
done	5002
1	2323
0	723

prune19.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes1.7s

Accuracy

44.3% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.7b

bsearch732.0ms

Steps

Iters	Range		Point
9	-1.0033578155902432	-1.1785608538762668e-07	-0.011756186125805182

simplify32.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end8.0ms

sample50.2s

Algorithm: halfpoints