Details

sample107.0ms

Algorithm

intervals

Results

42.0ms	53×	body	640	valid
19.0ms	139×	body	80	valid
17.0ms	26×	body	1280	valid
11.0ms	25×	body	320	valid
4.0ms	13×	body	160	valid

simplify112.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

112.0ms

(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize27.0ms

Local error

Found 3 expressions with local error:

1.4b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (+ x 1))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
35×	`times-frac`
29×	`add-sqr-sqrt`
17×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`add-cube-cbrt`
10×	`add-log-exp`
7×	`add-exp-log` `div-inv`
6×	`difference-of-squares`
5×	`add-cbrt-cube`
4×	`pow1` `associate-/r*`
3×	`frac-add` `insert-posit16` `associate-/l*`
2×	`associate-+l+` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `div-exp` `associate-/r/` `frac-sub` `flip-+` `flip--`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-+l-` `pow-flip` `inv-pow`

Counts

3 → 91

Calls

3 calls:

Slowest

177.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
31.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
14.0ms	(/ 1 (+ x 1))

series153.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

105.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
26.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
22.0ms	(/ 1 (+ x 1))

simplify6.6s

Counts

91 → 100

Calls

91 calls:

Slowest

624.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))
444.0ms	(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
420.0ms	(+ (* (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x))) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) 1))
358.0ms	(* (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))) (- x 1))
334.0ms	(* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))

prune870.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 3 expressions with local error:

1.4b	(+ (/ 1 (- x 1)) (- (/ 1 (+ x 1)) (/ 2 x)))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (+ x 1))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
35×	`times-frac`
29×	`add-sqr-sqrt`
17×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`add-cube-cbrt`
10×	`add-log-exp`
7×	`add-exp-log` `div-inv`
6×	`difference-of-squares`
5×	`add-cbrt-cube`
4×	`pow1` `associate-/r*`
3×	`frac-add` `insert-posit16` `associate-/l*`
2×	`associate-+r+` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `div-exp` `associate-/r/` `frac-sub` `flip-+` `flip--`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `associate-+r-` `frac-2neg` `1-exp` `pow-flip` `inv-pow`

Counts

3 → 91

Calls

3 calls:

Slowest

152.0ms	(+ (/ 1 (- x 1)) (- (/ 1 (+ x 1)) (/ 2 x)))
32.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
14.0ms	(/ 1 (+ x 1))

series194.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

143.0ms	(+ (/ 1 (- x 1)) (- (/ 1 (+ x 1)) (/ 2 x)))
31.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
20.0ms	(/ 1 (+ x 1))

simplify6.2s

Counts

91 → 100

Calls

91 calls:

Slowest

489.0ms	(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
413.0ms	(* (- x 1) (* (+ x 1) x))
410.0ms	(* (- x 1) (+ (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ x 1)) (/ 2 x)))))
406.0ms	(* (- x 1) (+ (/ 1 (+ x 1)) (/ 2 x)))
401.0ms	(+ (* 1 (+ (/ 1 (+ x 1)) (/ 2 x))) (* (- x 1) (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 2 x) (/ 2 x)))))

prune738.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

2.6b	(+ (/ 1 (- x 1)) (/ 1 (+ x 1)))
1.2b	(+ (+ (/ 1 (- x 1)) (/ 1 (+ x 1))) (/ -2 x))
0.0b	(/ 1 (+ x 1))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
48×	`times-frac`
46×	`distribute-lft-out`
20×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-log-exp`
9×	`div-inv`
8×	`distribute-lft-out--`
7×	`add-exp-log`
5×	`add-cbrt-cube` `frac-add` `flip-+`
4×	`pow1` `associate-/r*` `sum-log` `flip3-+` `associate-/r/`
3×	`insert-posit16` `associate-/l*`
2×	`+-commutative` `div-exp`
1×	`cbrt-undiv` `rec-exp` `associate-+l+` `clear-num` `frac-2neg` `1-exp` `pow-flip` `flip--` `inv-pow`

Counts

3 → 94

Calls

3 calls:

Slowest

212.0ms	(+ (+ (/ 1 (- x 1)) (/ 1 (+ x 1))) (/ -2 x))
51.0ms	(+ (/ 1 (- x 1)) (/ 1 (+ x 1)))
16.0ms	(/ 1 (+ x 1))

series207.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

113.0ms	(+ (+ (/ 1 (- x 1)) (/ 1 (+ x 1))) (/ -2 x))
79.0ms	(+ (/ 1 (- x 1)) (/ 1 (+ x 1)))
15.0ms	(/ 1 (+ x 1))

simplify6.3s

Counts

100 → 103

Calls

100 calls:

Slowest

826.0ms	(* (+ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (* (/ 1 (+ x 1)) (/ 1 (+ x 1))) (* (/ 1 (- x 1)) (/ 1 (+ x 1))))) x)
444.0ms	(+ (* 1 (+ x 1)) (* (- x 1) 1))
431.0ms	(/ (* (* 1 1) 1) (* (* (+ x 1) (+ x 1)) (+ x 1)))
323.0ms	(+ (* 2 (/ 1 (pow x 5))) (+ (* 2 (/ 1 (pow x 3))) (* 2 (/ 1 x))))
319.0ms	(- (+ (/ 1 (pow x 3)) (/ 1 x)) (/ 1 (pow x 2)))

prune767.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

15.8b	(+ (+ (+ (* -2 (* x x)) 2) (* x x)) (* x x))
15.1b	(+ (+ (* -2 (* x x)) 2) (* x x))
5.6b	(- (* x (+ x (* x x))) (+ x (* x x)))
0.1b	(* x (+ x (* x x)))

rewrite444.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-log-exp`
10×	`sum-log`
9×	`*-un-lft-identity` `flip3-+` `flip-+`
8×	`add-sqr-sqrt` `associate-*r/`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`associate-r`
4×	`frac-sub` `insert-posit16`
3×	`associate-l`
2×	`distribute-rgt-in` `+-commutative` `associate-+l+` `distribute-lft-in` `distribute-rgt-out` `diff-log` `associate--l+` `sub-div`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `pow-prod-down` `distribute-rgt1-in` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `associate--r+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

Slowest

311.0ms	(+ (+ (+ (* -2 (* x x)) 2) (* x x)) (* x x))
104.0ms	(+ (+ (* -2 (* x x)) 2) (* x x))
14.0ms	(* x (+ x (* x x)))
13.0ms	(- (* x (+ x (* x x))) (+ x (* x x)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

97.0ms	(* x (+ x (* x x)))
75.0ms	(- (* x (+ x (* x x))) (+ x (* x x)))
55.0ms	(+ (+ (* -2 (* x x)) 2) (* x x))
3.0ms	(+ (+ (+ (* -2 (* x x)) 2) (* x x)) (* x x))

simplify7.8s

Counts

54 → 91

Calls

54 calls:

Slowest

731.0ms	(* (+ (* x x) (- (* (* x x) (* x x)) (* x (* x x)))) (+ (* x x) (- (* (* x x) (* x x)) (* x (* x x)))))
540.0ms	(- (* x (+ (pow x 3) (pow (* x x) 3))) (+ (pow x 3) (pow (* x x) 3)))
507.0ms	(* (* (exp (+ (* -2 (* x x)) 2)) (exp (* x x))) (exp (* x x)))
506.0ms	(* (* (exp (* -2 (* x x))) (exp 2)) (exp (* x x)))
460.0ms	(- (* (* x (+ (pow x 3) (pow (* x x) 3))) (+ (* x x) (- (* (* x x) (* x x)) (* x (* x x))))) (* (+ (* x x) (- (* (* x x) (* x x)) (* x (* x x)))) (+ (pow x 3) (pow (* x x) 3))))

prune812.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

98.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 8.3b

bsearch103.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

870.0ms	1882×	body	640	valid
631.0ms	960×	body	320	valid
422.0ms	4089×	body	80	valid
322.0ms	591×	body	1280	valid
85.0ms	480×	body	160	valid