Details

sample88.0ms

Algorithm

intervals

Results

36.0ms	69×	body	1280	valid
18.0ms	50×	body	640	valid
12.0ms	171×	body	80	valid
8.0ms	31×	body	320	valid
2.0ms	12×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	16
3	16
2	14
1	11
0	5

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
4.7b	(- (exp x) 1)

rewrite51.0ms

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-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

34.0ms	(/ (- (exp x) 1) x)
16.0ms	(- (exp x) 1)

series87.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (- (exp x) 1) x)
23.0ms	(- (exp x) 1)

simplify2.8s

Counts

70 → 70

Iterations

Iter	Nodes
4	4417
3	1393
2	512
1	232
0	108

prune478.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
2×	`pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 42

Calls

2 calls:

42.0ms	(* x (+ (* 1/6 x) 1/2))
7.0ms	(* 1/6 x)

series96.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(* x (+ (* 1/6 x) 1/2))
24.0ms	(* 1/6 x)

simplify5.4s

Counts

48 → 48

Iterations

Iter	Nodes
4	7450
3	1901
2	511
1	186
0	72

prune420.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (exp (* x 3)) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
0.0b	(+ 1 (exp x))
0.0b	(exp (* x 3))
5.0b	(+ (exp (* x 3)) -1)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

74.0ms	(/ (+ (exp (* x 3)) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
9.0ms	(+ 1 (exp x))
8.0ms	(exp (* x 3))
24.0ms	(+ (exp (* x 3)) -1)

series143.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (exp (* x 3)) -1) (+ (* (exp x) (+ 1 (exp x))) 1))
15.0ms	(+ 1 (exp x))
10.0ms	(exp (* x 3))
19.0ms	(+ (exp (* x 3)) -1)

simplify2.9s

Counts

91 → 91

Iterations

Iter	Nodes
3	3449
2	1061
1	364
0	142

prune924.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1 (exp x)) (+ 1 (exp x)))
0.0b	(cbrt (* (* (+ 1 (exp x)) (+ 1 (exp x))) (+ 1 (exp x))))
0.0b	(exp (* x 3))
5.0b	(+ (exp (* x 3)) -1)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

34×	`flip3-+` `flip-+`
32×	`frac-times`
26×	`cbrt-div`
24×	`*-un-lft-identity`
16×	`associate-*l/`
11×	`add-sqr-sqrt` `pow1`
10×	`associate-*r/`
8×	`add-cube-cbrt` `add-log-exp`
7×	`distribute-lft-out`
6×	`add-cbrt-cube` `swap-sqr` `add-exp-log`
4×	`associate-r` `associate-l` `insert-posit16`
1×	`cbrt-prod` `pow2` `distribute-rgt-in` `+-commutative` `difference-of-sqr--1` `exp-lft-cube` `exp-prod` `sum-log` `distribute-lft-in` `pow-plus` `exp-to-pow` `pow1/3` `pow3` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 104

Calls

4 calls:

52.0ms	(* (+ 1 (exp x)) (+ 1 (exp x)))
55.0ms	(cbrt (* (* (+ 1 (exp x)) (+ 1 (exp x))) (+ 1 (exp x))))
8.0ms	(exp (* x 3))
16.0ms	(+ (exp (* x 3)) -1)

series87.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (+ 1 (exp x)) (+ 1 (exp x)))
16.0ms	(cbrt (* (* (+ 1 (exp x)) (+ 1 (exp x))) (+ 1 (exp x))))
11.0ms	(exp (* x 3))
30.0ms	(+ (exp (* x 3)) -1)

simplify1.4s

Counts

116 → 116

Iterations

Iter	Nodes
2	2395
1	612
0	195

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes93.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.4b

bsearch72.0ms

Steps

Iters	Range		Point
9	-0.0045708168411183105	-3.04125237332328e-12	-0.0001013307789888238

simplify10.0ms

Iterations

Iter	Nodes
2	35
1	35
0	25

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	2254×	body	1280	valid
581.0ms	1718×	body	640	valid
369.0ms	5354×	body	80	valid
191.0ms	878×	body	320	valid
52.0ms	408×	body	160	valid