Details

sample100.0ms

Algorithm

intervals

Results

56.0ms

762×

body

valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2733
6	751
5	308
4	183
3	84
2	39
1	18
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
7.7b	(/ (* (cosh x) (/ y x)) z)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 60

Calls

2 calls:

22.0ms	(* (cosh x) (/ y x))
11.0ms	(/ (* (cosh x) (/ y x)) z)

series268.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(* (cosh x) (/ y x))
151.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.6s

Counts

66 → 66

Iterations

Iter	Nodes
done	5002
2	1310
1	345
0	137

prune343.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z)
0.0b	(/ 1/2 (exp x))
0.2b	(* y (/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z))
5.0b	(/ (* y (/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z)) x)

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

51.0ms	(/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z)
5.0ms	(/ 1/2 (exp x))
79.0ms	(* y (/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z))
39.0ms	(/ (* y (/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z)) x)

series434.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z)
20.0ms	(/ 1/2 (exp x))
140.0ms	(* y (/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z))
162.0ms	(/ (* y (/ (+ (/ 1/2 (exp x)) (* 1/2 (exp x))) z)) x)

simplify2.4s

Counts

131 → 131

Iterations

Iter	Nodes
done	5002
2	2247
1	537
0	216

prune898.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

1.8b	(/ (* 1/2 (* x x)) (/ z y))
5.0b	(/ (+ (/ (* 1/2 (* x x)) (/ z y)) (/ y z)) x)

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
33×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
16×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-/l*`
4×	`div-inv` `distribute-lft-out`
3×	`associate-/l/`
2×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
1×	`flip3-+` `frac-add` `associate-/r/` `flip-+`

Counts

2 → 84

Calls

2 calls:

39.0ms	(/ (* 1/2 (* x x)) (/ z y))
128.0ms	(/ (+ (/ (* 1/2 (* x x)) (/ z y)) (/ y z)) x)

series154.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (* 1/2 (* x x)) (/ z y))
86.0ms	(/ (+ (/ (* 1/2 (* x x)) (/ z y)) (/ y z)) x)

simplify1.8s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1892
1	546
0	189

prune664.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) y)
5.5b	(/ (* (cosh x) y) (* z x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

12.0ms	(* (cosh x) y)
20.0ms	(/ (* (cosh x) y) (* z x))

series294.0ms

Counts

2 → 6

Calls

2 calls:

106.0ms	(* (cosh x) y)
188.0ms	(/ (* (cosh x) y) (* z x))

simplify1.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	5013
2	1254
1	275
0	102

prune237.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes262.0ms

Accuracy

94.5% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 7.0b

bsearch126.0ms

Steps

Iters	Range		Point
5	1.604812628462419e+24	4.63068866439605e+24	1.6348041522647664e+24
10	-5.495080658455137e-22	-3.125403883490737e-39	-1.2595471582822284e-30

simplify4.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s

22530×

body

valid