Details

sample36.0ms

Algorithm

intervals

Results

19.0ms

631×

body

valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	8
1	18	8
2	40	8
3	99	8
4	221	8
5	405	8
6	727	8
7	2070	8
8	4775	8
done	5001	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
8.2b	(/ (* (cosh x) (/ y x)) z)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `cosh-def` `prod-exp` `cbrt-unprod`
3×	`associate-l` `associate-/r*` `associate-/l/`
2×	`expm1-log1p-u` `frac-times` `associate-r/` `associate-l/` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

2 → 64

Calls

2 calls:

8.0ms	(* (cosh x) (/ y x))
6.0ms	(/ (* (cosh x) (/ y x)) z)

series192.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (cosh x) (/ y x))
114.0ms	(/ (* (cosh x) (/ y x)) z)

simplify525.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	141	739
1	360	701
2	1512	600
done	5000	600

prune162.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) y)
5.6b	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log` `add-cbrt-cube`
10×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`cbrt-undiv` `add-cube-cbrt` `div-exp`
5×	`pow1` `add-log-exp`
4×	`associate-l` `associate-*l/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `associate-r` `flip-+` `log1p-expm1-u`
2×	`associate-/l/` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

6.0ms	(+ (exp x) (exp (- x)))
21.0ms	(* (+ (exp x) (exp (- x))) y)
14.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

series174.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (exp x) (exp (- x)))
53.0ms	(* (+ (exp x) (exp (- x))) y)
98.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

simplify958.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (174.0ms)

Iter	Nodes	Cost
0	145	1158
1	439	1102
2	2305	859
done	5000	859

prune184.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) (exp (- x))) y) z)
0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) y)
6.3b	(/ (/ (* (+ (exp x) (exp (- x))) y) z) (* 2 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
17×	`*-un-lft-identity`
16×	`times-frac`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `associate-l/` `associate-/r` `log1p-expm1-u` `div-inv`
3×	`fma-def` `flip3-+` `associate-r` `flip-+` `associate-/l/`
2×	`frac-2neg` `clear-num` `distribute-lft-out`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

9.0ms	(/ (* (+ (exp x) (exp (- x))) y) z)
6.0ms	(+ (exp x) (exp (- x)))
21.0ms	(* (+ (exp x) (exp (- x))) y)
12.0ms	(/ (/ (* (+ (exp x) (exp (- x))) y) z) (* 2 x))

series233.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (* (+ (exp x) (exp (- x))) y) z)
22.0ms	(+ (exp x) (exp (- x)))
55.0ms	(* (+ (exp x) (exp (- x))) y)
90.0ms	(/ (/ (* (+ (exp x) (exp (- x))) y) z) (* 2 x))

simplify830.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (189.0ms)

Iter	Nodes	Cost
0	190	1712
1	516	1634
2	2434	1336
done	5000	1336

prune299.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) y)
0.3b	(/ (/ 1 z) x)
5.9b	(* (/ (* (+ (exp x) (exp (- x))) y) 2) (/ (/ 1 z) x))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

149×	`times-frac`
100×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
86×	`add-cube-cbrt`
75×	`add-exp-log`
47×	`add-cbrt-cube`
46×	`associate-r`
34×	`div-exp`
21×	`prod-exp`
18×	`cbrt-undiv`
13×	`cbrt-unprod` `associate-/l*`
11×	`associate-l`
10×	`div-inv`
8×	`pow1`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`fma-def` `associate-l/` `associate-/r`
2×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `distribute-lft-out`
1×	`+-commutative` `frac-times` `frac-2neg` `associate-*r/` `clear-num` `sum-log` `associate-/l/`

Counts

4 → 206

Calls

4 calls:

6.0ms	(+ (exp x) (exp (- x)))
24.0ms	(* (+ (exp x) (exp (- x))) y)
6.0ms	(/ (/ 1 z) x)
48.0ms	(* (/ (* (+ (exp x) (exp (- x))) y) 2) (/ (/ 1 z) x))

series189.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (exp x) (exp (- x)))
60.0ms	(* (+ (exp x) (exp (- x))) y)
10.0ms	(/ (/ 1 z) x)
95.0ms	(* (/ (* (+ (exp x) (exp (- x))) y) 2) (/ (/ 1 z) x))

simplify2.1s

Counts

218 → 218

Iterations

Useful iterations: 2 (405.0ms)

Iter	Nodes	Cost
0	337	3497
1	1011	3144
2	4369	2624
done	5000	2624

prune519.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes195.0ms

Accuracy

96.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 6.8b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	22	58
1	29	45
done	29	45

end0.0ms

sample1.1s

Algorithm

intervals

Results

601.0ms

22339×

body

valid