Details

sample57.0ms

Algorithm

intervals

Results

21.0ms	66×	body	1280	valid
18.0ms	45×	body	640	valid
7.0ms	121×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify41.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

41.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize13.0ms

Local error

Found 3 expressions with local error:

2.9b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

Slowest

74.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
29.0ms	(/ (+ x 1) (- x 1))
16.0ms	(/ x (+ x 1))

series188.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

109.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
45.0ms	(/ x (+ x 1))
34.0ms	(/ (+ x 1) (- x 1))

simplify5.1m

Counts

1382 → 762

Calls

1382 calls:

Slowest

883.0ms	(fma (/ (sqrt x) 1) (/ (sqrt x) (+ x 1)) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
815.0ms	(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
807.0ms	(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
803.0ms	(fma (- (/ (+ x 1) (sqrt (- x 1)))) (/ 1 (sqrt (- x 1))) (* (/ (+ x 1) (sqrt (- x 1))) (/ 1 (sqrt (- x 1)))))
802.0ms	(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

prune4.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

5.8b	(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))
0.7b	(/ -1 (* x x))
0.1b	(/ (/ -1 x) (* x x))
0.0b	(+ (/ -1 x) (/ (/ -1 x) (* x x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
29×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
13×	`fma-def`
8×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod`
2×	`clear-num` `associate-/r*` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3-+` `frac-add` `flip-+` `fma-udef` `distribute-lft-out` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

Slowest

15.0ms	(+ (/ -1 x) (/ (/ -1 x) (* x x)))
10.0ms	(/ (/ -1 x) (* x x))
6.0ms	(/ -1 (* x x))
0.0ms	(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

53.0ms	(+ (/ -1 x) (/ (/ -1 x) (* x x)))
33.0ms	(/ (/ -1 x) (* x x))
29.0ms	(/ -1 (* x x))
28.0ms	(fma 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))) (/ -1 (* x x)))

simplify3.1s

Counts

84 → 125

Calls

84 calls:

Slowest

285.0ms	(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))
250.0ms	(/ (* (* -1 -1) -1) (* (* (* x x) (* x x)) (* x x)))
182.0ms	(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
175.0ms	(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
175.0ms	(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune649.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

5.6b	(+ (* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x)))) (/ -1 (* x x)))
0.7b	(/ -1 (* x x))
0.2b	(* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))))
0.1b	(/ (/ -1 x) (* x x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cbrt-cube` `add-exp-log`
22×	`add-cube-cbrt`
16×	`associate-/l*`
8×	`cbrt-undiv` `div-exp`
6×	`pow1` `associate-*r/` `add-log-exp`
5×	`frac-add`
4×	`expm1-log1p-u` `associate-r` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`flip3-+` `associate-l` `flip-+`
2×	`distribute-rgt-in` `associate-+l+` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `fma-def` `pow-prod-down` `*-commutative` `distribute-lft-out` `unswap-sqr` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

Slowest

49.0ms	(* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))))
22.0ms	(+ (* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x)))) (/ -1 (* x x)))
10.0ms	(/ (/ -1 x) (* x x))
6.0ms	(/ -1 (* x x))

series161.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

71.0ms	(* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x))))
33.0ms	(/ (/ -1 x) (* x x))
30.0ms	(+ (* 3 (+ (/ -1 x) (/ (/ -1 x) (* x x)))) (/ -1 (* x x)))
26.0ms	(/ -1 (* x x))

simplify6.6s

Counts

94 → 132

Calls

94 calls:

Slowest

904.0ms	(* (- (/ -1 x) (/ (/ -1 x) (* x x))) (* x x))
571.0ms	(* (+ (* (/ -1 x) (/ -1 x)) (- (* (/ (/ -1 x) (* x x)) (/ (/ -1 x) (* x x))) (* (/ -1 x) (/ (/ -1 x) (* x x))))) (* x x))
301.0ms	(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
298.0ms	(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))
294.0ms	(- (+ (* 3 (/ 1 (pow x 3))) (* 3 (/ 1 x))))

prune619.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b	(+ (+ (/ -3 (* (* x x) x)) (/ -3 x)) (/ -1 (* x x)))
0.7b	(/ -1 (* x x))
0.1b	(/ -3 (* (* x x) x))
0.1b	(* (* x x) x)

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
23×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`times-frac`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
10×	`fma-def`
9×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`pow-plus` `pow-prod-up` `associate-/l*`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out`
4×	`expm1-log1p-u` `distribute-rgt-out` `frac-add` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`sum-log` `associate-r` `pow-prod-down`
2×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `pow-sqr` `flip-+`
1×	`+-commutative` `associate-+l+` `distribute-lft1-in` `associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

Slowest

214.0ms	(+ (+ (/ -3 (* (* x x) x)) (/ -3 x)) (/ -1 (* x x)))
14.0ms	(* (* x x) x)
14.0ms	(/ -3 (* (* x x) x))
6.0ms	(/ -1 (* x x))

series130.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

41.0ms	(/ -3 (* (* x x) x))
35.0ms	(* (* x x) x)
27.0ms	(+ (+ (/ -3 (* (* x x) x)) (/ -3 x)) (/ -1 (* x x)))
26.0ms	(/ -1 (* x x))

simplify4.4s

Counts

70 → 124

Calls

70 calls:

Slowest

458.0ms	(+ (* (- (* (/ -3 (* (* x x) x)) (/ -3 (* (* x x) x))) (* (/ -3 x) (/ -3 x))) (* x x)) (* (- (/ -3 (* (* x x) x)) (/ -3 x)) -1))
399.0ms	(* (- (/ -3 (* (* x x) x)) (/ -3 x)) (* x x))
321.0ms	(* (+ (* (/ -3 (* (* x x) x)) (/ -3 (* (* x x) x))) (- (* (/ -3 x) (/ -3 x)) (* (/ -3 (* (* x x) x)) (/ -3 x)))) (* x x))
300.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
285.0ms	(/ (* (* -1 -1) -1) (* (* (* x x) x) (* (* x x) x)))

prune588.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch160.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

761.0ms	1636×	body	1280	valid
314.0ms	1305×	body	640	valid
259.0ms	4072×	body	80	valid
162.0ms	634×	body	320	valid
63.0ms	353×	body	160	valid