Details

sample90.0ms

Algorithm

intervals

Results

30.0ms	77×	body	10240	exit
25.0ms	73×	body	1280	valid
14.0ms	54×	body	640	valid
5.0ms	92×	body	80	valid
3.0ms	22×	body	320	valid
2.0ms	15×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	9
2	9
1	8
0	5

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1))
4.8b	(- (exp x) 1)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

13.0ms	(/ (exp x) (- (exp x) 1))
9.0ms	(- (exp x) 1)

series64.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (exp x) (- (exp x) 1))
29.0ms	(- (exp x) 1)

simplify2.4s

Counts

69 → 69

Iterations

Iter	Nodes
4	3966
3	1266
2	468
1	196
0	101

prune422.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.3b	(* 1/12 x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l`
2×	`insert-posit16`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

34.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
5.0ms	(* 1/12 x)

series53.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
27.0ms	(* 1/12 x)

simplify11.0s

Counts

39 → 39

Iterations

Iter	Nodes
4	10077
3	1691
2	442
1	151
0	60

prune263.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (exp (* x 3)) -1) (+ (* (+ (exp x) 1) (exp x)) 1))
0.0b	(* (+ (exp x) 1) (exp x))
0.0b	(exp (* x 3))
4.8b	(+ (exp (* x 3)) -1)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-cbrt-cube` `add-log-exp`
7×	`add-exp-log`
6×	`pow1` `distribute-lft-out`
5×	`difference-of-sqr--1` `associate-/l*`
4×	`flip3-+` `associate-l` `flip-+` `insert-posit16`
3×	`associate-/r` `associate-r*`
2×	`associate-*l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `exp-lft-cube` `exp-prod` `clear-num` `sum-log` `frac-2neg` `exp-to-pow` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr` `rem-exp-log`

Counts

4 → 88

Calls

4 calls:

44.0ms	(/ (+ (exp (* x 3)) -1) (+ (* (+ (exp x) 1) (exp x)) 1))
26.0ms	(* (+ (exp x) 1) (exp x))
7.0ms	(exp (* x 3))
9.0ms	(+ (exp (* x 3)) -1)

series156.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (exp (* x 3)) -1) (+ (* (+ (exp x) 1) (exp x)) 1))
31.0ms	(* (+ (exp x) 1) (exp x))
7.0ms	(exp (* x 3))
18.0ms	(+ (exp (* x 3)) -1)

simplify2.3s

Counts

100 → 100

Iterations

Iter	Nodes
3	3089
2	1085
1	383
0	155

prune924.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x 3))
0.0b	(/ (/ (+ (exp (* x 3)) -1) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1))) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1)))
0.1b	(/ (+ (exp (* x 3)) -1) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1)))
4.8b	(+ (exp (* x 3)) -1)

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

456×	`times-frac`
316×	`*-un-lft-identity`
266×	`add-sqr-sqrt`
234×	`sqrt-prod`
216×	`add-cube-cbrt`
50×	`difference-of-sqr--1` `distribute-lft-out`
41×	`associate-/l*`
18×	`sqrt-div` `associate-/r/`
12×	`associate-/r*`
11×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
9×	`div-inv`
8×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp` `insert-posit16`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `exp-lft-cube` `exp-prod` `sum-log` `exp-to-pow` `rem-exp-log`

Counts

4 → 360

Calls

4 calls:

9.0ms	(exp (* x 3))
119.0ms	(/ (/ (+ (exp (* x 3)) -1) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1))) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1)))
66.0ms	(/ (+ (exp (* x 3)) -1) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1)))
13.0ms	(+ (exp (* x 3)) -1)

series307.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* x 3))
79.0ms	(/ (/ (+ (exp (* x 3)) -1) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1))) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1)))
194.0ms	(/ (+ (exp (* x 3)) -1) (sqrt (+ (* (+ (exp x) 1) (exp x)) 1)))
21.0ms	(+ (exp (* x 3)) -1)

simplify1.6s

Counts

372 → 372

Iterations

Iter	Nodes
2	2442
1	940
0	415

prune4.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 21.5b

bsearch1.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	43
1	43
0	30

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	2563×	body	10240	exit
1.1s	2262×	body	1280	valid
599.0ms	1611×	body	640	valid
179.0ms	858×	body	320	valid
175.0ms	2872×	body	80	valid
76.0ms	399×	body	160	valid