Details

sample144.0ms

Algorithm

intervals

Results

106.0ms	192×	body	1280	valid
13.0ms	230×	body	80	valid
10.0ms	30×	body	640	valid
4.0ms	22×	body	320	valid
1.0ms	6×	body	160	valid

simplify57.0ms

Calls

1 calls:

Slowest

57.0ms

(+ (- (exp x) 2) (exp (- x)))

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.9b

localize11.0ms

Local error

Found 2 expressions with local error:

3.5b	(+ (- (exp x) 2) (exp (- x)))
0.0b	(- (exp x) 2)

rewrite496.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`neg-sub0` `exp-neg` `expm1-log1p-u` `pow1` `sum-log` `sub-neg` `add-cbrt-cube` `exp-diff` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+`

Calls

2 calls:

Slowest

486.0ms	(+ (- (exp x) 2) (exp (- x)))
9.0ms	(- (exp x) 2)

series89.0ms

Calls

2 calls:

Slowest

75.0ms	(+ (- (exp x) 2) (exp (- x)))
13.0ms	(- (exp x) 2)

simplify3.4s

Calls

57 calls:

Slowest

455.0ms	(+ (* (- (* (exp x) (exp x)) (* 2 2)) (exp x)) (* (+ (exp x) 2) (exp 0)))
319.0ms	(+ (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) 1))
296.0ms	(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
270.0ms	(+ (* (- (pow (exp x) 3) (pow 2 3)) (exp x)) (* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (exp 0)))
183.0ms	(* (+ (* (exp x) (exp x)) (+ (* 2 2) (* (exp x) 2))) (exp x))

prune621.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(* (* (* x x) (* x x)) 1/360)
0.0b	(fma (* (* (* x x) (* x x)) 1/360) (* x x) (fma (* (* x x) (* x x)) 1/12 (* x x)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

244×	`pow1`
72×	`pow-prod-up`
59×	`pow-prod-down`
46×	`add-cbrt-cube` `add-exp-log`
44×	`pow-sqr`
36×	`pow-plus`
29×	`prod-exp` `cbrt-unprod`
26×	`pow2`
6×	`add-sqr-sqrt`
5×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`fma-udef`

Calls

4 calls:

Slowest

125.0ms	(* (* (* x x) (* x x)) 1/360)
44.0ms	(* (* x x) (* x x))
30.0ms	(* (* x x) (* x x))
0.0ms	(fma (* (* (* x x) (* x x)) 1/360) (* x x) (fma (* (* x x) (* x x)) 1/12 (* x x)))

series261.0ms

Calls

4 calls:

Slowest

98.0ms	(fma (* (* (* x x) (* x x)) 1/360) (* x x) (fma (* (* x x) (* x x)) 1/12 (* x x)))
69.0ms	(* (* (* x x) (* x x)) 1/360)
51.0ms	(* (* x x) (* x x))
43.0ms	(* (* x x) (* x x))

simplify7.6s

Calls

166 calls:

Slowest

440.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
426.0ms	(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 1/360 1/360) 1/360))
394.0ms	(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
382.0ms	(* (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (* (* x x) (* x x))) (* (* 1/360 1/360) 1/360))
380.0ms	(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 1/360 1/360) 1/360))

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

3.1b	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)
0.0b	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (* (+ (exp x) 2) (exp x)))
0.0b	(* (exp x) (exp x))
0.0b	(* (+ (exp x) 2) (exp x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`exp-prod` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube`
9×	`add-exp-log`
7×	`associate-l`
6×	`associate-r`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-*l/` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `swap-sqr` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `*-commutative` `flip-+` `unswap-sqr`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `fma-udef` `div-inv` `distribute-lft-out`

Calls

4 calls:

Slowest

33.0ms	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (* (+ (exp x) 2) (exp x)))
26.0ms	(* (exp x) (exp x))
25.0ms	(* (+ (exp x) 2) (exp x))
1.0ms	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)

series324.0ms

Calls

4 calls:

Slowest

172.0ms	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (* (+ (exp x) 2) (exp x)))
96.0ms	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)
36.0ms	(* (+ (exp x) 2) (exp x))
19.0ms	(* (exp x) (exp x))

simplify5.6s

Calls

77 calls:

Slowest

622.0ms	(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
569.0ms	(* (+ (pow (exp x) 3) (pow 2 3)) (exp x))
385.0ms	(/ (* (* (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (fma (+ (* (exp x) (exp x)) -3) (exp x) 2)) (fma (+ (* (exp x) (exp x)) -3) (exp x) 2)) (* (* (* (+ (exp x) 2) (exp x)) (* (+ (exp x) 2) (exp x))) (* (+ (exp x) 2) (exp x))))
384.0ms	(* (- (* (exp x) (exp x)) (* 2 2)) (exp x))
291.0ms	(- (+ (pow (exp x) 3) 2) (* 3 (exp x)))

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

3.1b	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)
0.0b	(/ (/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (+ (exp x) 2)) (exp x))
0.0b	(* (exp x) (exp x))
0.0b	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (+ (exp x) 2))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
106×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
21×	`associate-/l*`
18×	`exp-prod`
16×	`distribute-lft-out`
13×	`add-cbrt-cube`
11×	`pow1`
10×	`associate-/r/`
9×	`add-exp-log`
7×	`associate-/r*`
6×	`div-inv`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `associate-/l/`

Calls

4 calls:

Slowest

41.0ms	(/ (/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (+ (exp x) 2)) (exp x))
27.0ms	(* (exp x) (exp x))
22.0ms	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (+ (exp x) 2))
1.0ms	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)

series382.0ms

Calls

4 calls:

Slowest

174.0ms	(/ (/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (+ (exp x) 2)) (exp x))
126.0ms	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (+ (exp x) 2))
67.0ms	(fma (+ (* (exp x) (exp x)) -3) (exp x) 2)
15.0ms	(* (exp x) (exp x))

simplify20.2s

Calls

217 calls:

Slowest

532.0ms	(/ (fma (+ (* (exp x) (exp x)) -3) (exp x) 2) (+ (pow (exp x) 3) (pow 2 3)))
476.0ms	(/ (+ (* (exp x) (exp x)) (- (* 2 2) (* (exp x) 2))) (exp x))
432.0ms	(/ (/ (* (cbrt (fma (+ (* (exp x) (exp x)) -3) (exp x) 2)) (cbrt (fma (+ (* (exp x) (exp x)) -3) (exp x) 2))) (* (cbrt (+ (exp x) 2)) (cbrt (+ (exp x) 2)))) (* (cbrt (exp x)) (cbrt (exp x))))
413.0ms	(/ (- (+ (pow (exp x) 3) 2) (* 3 (exp x))) (+ (exp x) 2))
374.0ms	(/ (- (+ (pow (exp x) 3) 2) (* 3 (exp x))) (+ (exp x) 2))

prune1.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch2.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.9s	5600×	body	1280	valid
588.0ms	8153×	body	80	valid
396.0ms	1242×	body	640	valid
136.0ms	670×	body	320	valid
42.0ms	306×	body	160	valid