Details

sample52.0ms

Algorithm

intervals

Results

23.0ms	78×	body	1280	valid
10.0ms	51×	body	640	valid
7.0ms	169×	body	80	valid
4.0ms	26×	body	320	valid
1.0ms	14×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
3	18
2	16
1	13
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
3.4b	(- (exp x) 1)

rewrite38.0ms

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:

28.0ms	(/ (- (exp x) 1) x)
8.0ms	(- (exp x) 1)

series59.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- (exp x) 1) x)
16.0ms	(- (exp x) 1)

simplify722.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	976
1	262
0	108

prune304.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (* 1/6 x))
0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

4.0ms	(+ 1/2 (* 1/6 x))
15.0ms	(* x (+ 1/2 (* 1/6 x)))
11.0ms	(* 1/6 x)

series186.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(+ 1/2 (* 1/6 x))
93.0ms	(* x (+ 1/2 (* 1/6 x)))
24.0ms	(* 1/6 x)

simplify1.0s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
2	1004
1	232
0	81

prune175.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (exp x))
0.0b	(/ (+ (exp (+ (+ x x) x)) -1) (+ 1 (* (exp x) (+ 1 (exp x)))))
0.0b	(/ (/ (+ (exp (+ (+ x x) x)) -1) (+ 1 (* (exp x) (+ 1 (exp x))))) x)
3.3b	(+ (exp (+ (+ x x) x)) -1)

rewrite856.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
108×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
26×	`associate-/l*`
18×	`distribute-lft-out`
17×	`difference-of-sqr--1`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
8×	`flip3-+` `flip-+` `add-log-exp`
6×	`associate-/r*` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp` `insert-posit16`
3×	`associate-/l/`
2×	`+-commutative` `clear-num` `sum-log` `frac-2neg`

Counts

4 → 170

Calls

4 calls:

6.0ms	(+ 1 (exp x))
393.0ms	(/ (+ (exp (+ (+ x x) x)) -1) (+ 1 (* (exp x) (+ 1 (exp x)))))
333.0ms	(/ (/ (+ (exp (+ (+ x x) x)) -1) (+ 1 (* (exp x) (+ 1 (exp x))))) x)
118.0ms	(+ (exp (+ (+ x x) x)) -1)

series272.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ 1 (exp x))
78.0ms	(/ (+ (exp (+ (+ x x) x)) -1) (+ 1 (* (exp x) (+ 1 (exp x)))))
144.0ms	(/ (/ (+ (exp (+ (+ x x) x)) -1) (+ 1 (* (exp x) (+ 1 (exp x))))) x)
37.0ms	(+ (exp (+ (+ x x) x)) -1)

simplify2.6s

Counts

182 → 182

Iterations

Iter	Nodes
done	5001
2	4240
1	782
0	288

prune818.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(* (exp x) (exp x))
0.3b	(+ (* 3 x) (+ (* 3 x) (* 3 x)))
3.2b	(+ (exp (+ (* 3 x) (+ (* 3 x) (* 3 x)))) -1)

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

36×	`exp-prod`
29×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`pow1`
11×	`add-log-exp`
8×	`add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`sum-log` `add-exp-log` `insert-posit16`
3×	`distribute-lft-out`
2×	`pow2` `+-commutative` `flip3-+` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`difference-of-sqr--1` `associate-+r+` `count-2` `distribute-rgt1-in`

Counts

4 → 100

Calls

4 calls:

13.0ms	(* (exp x) (exp x))
19.0ms	(* (exp x) (exp x))
31.0ms	(+ (* 3 x) (+ (* 3 x) (* 3 x)))
120.0ms	(+ (exp (+ (* 3 x) (+ (* 3 x) (* 3 x)))) -1)

series120.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (exp x) (exp x))
23.0ms	(* (exp x) (exp x))
48.0ms	(+ (* 3 x) (+ (* 3 x) (* 3 x)))
28.0ms	(+ (exp (+ (* 3 x) (+ (* 3 x) (* 3 x)))) -1)

simplify2.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
2	1873
1	322
0	114

prune450.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.8b

bsearch66.0ms

Steps

Iters	Range		Point
10	-0.00010358510568112945	-1.790535254998819e-16	-7.91242022931417e-05

simplify8.0ms

Iterations

Iter	Nodes
done	52
1	52
0	35

end0.0ms

sample2.1s

Algorithm

intervals

Results

870.0ms	2164×	body	1280	valid
502.0ms	1661×	body	640	valid
334.0ms	5551×	body	80	valid
175.0ms	834×	body	320	valid
70.0ms	425×	body	160	valid