Details

sample64.0ms

Algorithm

intervals

Results

31.0ms

704×

body

valid

simplify7.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	18	8
2	41	8
3	102	8
4	220	8
5	368	8
6	574	8
7	1186	8
8	3410	8
done	5000	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
8.0b	(/ (* (cosh x) (/ y x)) z)

rewrite37.0ms

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×	`frac-times` `associate-r/` `associate-l/` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

2 → 60

Calls

2 calls:

15.0ms	(* (cosh x) (/ y x))
20.0ms	(/ (* (cosh x) (/ y x)) z)

series209.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* (cosh x) (/ y x))
126.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.3s

Counts

66 → 66

Iterations

Useful iterations: 2 (238.0ms)

Iter	Nodes	Cost
0	137	707
1	331	670
2	1289	570
done	5000	570

prune220.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* y (* 1/2 (+ (exp x) (exp (- x)))))
5.3b	(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log` `add-cbrt-cube`
12×	`prod-exp` `cbrt-unprod`
8×	`pow1` `associate-*r/`
6×	`cbrt-undiv` `*-un-lft-identity` `div-exp`
5×	`add-log-exp`
4×	`distribute-rgt-in` `add-sqr-sqrt` `add-cube-cbrt` `distribute-lft-in`
3×	`flip3-+` `associate-l` `pow-prod-down` `flip-+`
2×	`associate-/l/`
1×	`+-commutative` `frac-2neg` `times-frac` `associate-r` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

3 → 63

Calls

3 calls:

14.0ms	(+ (exp x) (exp (- x)))
64.0ms	(* y (* 1/2 (+ (exp x) (exp (- x)))))
71.0ms	(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

series253.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (exp x) (exp (- x)))
84.0ms	(* y (* 1/2 (+ (exp x) (exp (- x)))))
135.0ms	(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	146	1186
1	416	1122
2	2333	871
done	5000	870

prune217.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/2 (/ (* x y) z)) (/ y (* x z)))
0.0b	(* 1/2 (/ (* x y) z))
4.1b	(/ (* x y) z)
5.3b	(/ y (* x z))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`associate-/r` `associate-/l`
3×	`associate-l` `div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num`
1×	`+-commutative` `flip3-+` `pow-prod-down` `frac-add` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

22.0ms	(+ (* 1/2 (/ (* x y) z)) (/ y (* x z)))
19.0ms	(* 1/2 (/ (* x y) z))
10.0ms	(/ (* x y) z)
19.0ms	(/ y (* x z))

series176.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ (* 1/2 (/ (* x y) z)) (/ y (* x z)))
45.0ms	(* 1/2 (/ (* x y) z))
32.0ms	(/ (* x y) z)
26.0ms	(/ y (* x z))

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	133	985
1	349	918
2	1256	810
done	5001	809

prune218.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) z)
0.0b	(* y (* 1/2 (+ (exp x) (exp (- x)))))
7.2b	(/ (/ (* y (* 1/2 (+ (exp x) (exp (- x))))) z) x)

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
32×	`add-exp-log` `add-cbrt-cube`
25×	`*-un-lft-identity`
23×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
8×	`associate-r/` `associate-/l`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in`
3×	`flip3-+` `associate-l` `pow-prod-down` `flip-+` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-r` `sum-log` `*-commutative` `distribute-lft-out`

Counts

4 → 111

Calls

4 calls:

12.0ms	(+ (exp x) (exp (- x)))
85.0ms	(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) z)
81.0ms	(* y (* 1/2 (+ (exp x) (exp (- x)))))
71.0ms	(/ (/ (* y (* 1/2 (+ (exp x) (exp (- x))))) z) x)

series308.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (exp x) (exp (- x)))
115.0ms	(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) z)
56.0ms	(* y (* 1/2 (+ (exp x) (exp (- x)))))
110.0ms	(/ (/ (* y (* 1/2 (+ (exp x) (exp (- x))))) z) x)

simplify1.3s

Counts

123 → 123

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	220	2160
1	562	2064
2	2399	1772
done	5001	1771

prune334.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes246.0ms

Accuracy

96.1% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 7.0b

bsearch99.0ms

Steps

Iters	Range		Point
5	1.4016864363292013e-27	2.8214275147623435e-27	2.5406453345129323e-27
9	-1.4246018234571108e+20	-433755940707546.5	-7446916366273207.0

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	44
1	30	31
done	30	31

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s

22270×

body

valid