Details

sample350.0ms

Algorithm

intervals

Results

115.0ms	60×	body	10240	exit
80.0ms	334×	body	80	valid
69.0ms	45×	body	1280	valid
45.0ms	48×	body	640	valid
15.0ms	23×	body	320	valid
3.0ms	8×	body	160	valid

simplify332.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

332.0ms

(/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize58.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b	(* x (+ eps -1))
0.0b	(* x (+ eps -1))
0.0b	(/ (exp (* x (- -1 eps))) eps)

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
21×	`times-frac`
20×	`add-cube-cbrt`
16×	`exp-sum` `add-log-exp`
10×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `associate-r`
9×	`add-exp-log`
8×	`pow1`
7×	`associate-/l*`
6×	`diff-log` `associate-l` `distribute-lft-out--`
4×	`flip3-+` `associate-*r/` `frac-sub` `flip-+` `insert-posit16` `distribute-lft-out`
3×	`associate-/r*` `flip3--` `flip--`
2×	`difference-of-sqr--1` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate--l+` `div-inv` `associate--r-` `difference-of-squares`

Counts

4 → 123

Calls

4 calls:

Slowest

134.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
15.0ms	(* x (+ eps -1))
14.0ms	(* x (+ eps -1))
12.0ms	(/ (exp (* x (- -1 eps))) eps)

series274.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

142.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
49.0ms	(* x (+ eps -1))
49.0ms	(* x (+ eps -1))
34.0ms	(/ (exp (* x (- -1 eps))) eps)

simplify17.2s

Counts

118 → 135

Calls

118 calls:

Slowest

766.0ms	(- (* (+ (pow (exp (* x (+ eps -1))) 3) (pow (/ (exp (* x (+ eps -1))) eps) 3)) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (+ (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (- (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps)) (* (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
668.0ms	(- (* (- (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps))) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (- (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
504.0ms	(- (* (+ (pow (exp (* x (+ eps -1))) 3) (pow (/ (exp (* x (+ eps -1))) eps) 3)) (+ (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (* (+ (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (- (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps)) (* (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)))) (- (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))))))
411.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
376.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

6.6b	(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
0.1b	(* (* x (* x x)) -2/3)
0.1b	(* x (* x x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `pow-prod-up` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`diff-log` `insert-posit16`
2×	`sub-neg` `associate--l+` `*-commutative`
1×	`associate--l-` `pow2` `pow-plus` `flip3--` `cube-unmult` `pow-sqr` `flip--` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

Slowest

56.0ms	(* (* x (* x x)) -2/3)
45.0ms	(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
24.0ms	(* x (* x x))

series151.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

52.0ms	(* (* x (* x x)) -2/3)
49.0ms	(* x (* x x))
49.0ms	(- (- 2 (* x x)) (* (* x (* x x)) -2/3))

simplify4.2s

Counts

36 → 73

Calls

36 calls:

Slowest

538.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
495.0ms	(/ (/ (exp 2) (exp (* x x))) (exp (* (* x (* x x)) -2/3)))
422.0ms	(* (* (* (* x (* x x)) (* x (* x x))) (* x (* x x))) (* (* -2/3 -2/3) -2/3))
408.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
361.0ms	(+ (+ (log x) (log (* x x))) (log -2/3))

prune640.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 3 expressions with local error:

8.3b	(+ (* x x) (* (* x (* x x)) -2/3))
0.1b	(* (* x (* x x)) -2/3)
0.1b	(* x (* x x))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `pow-prod-up` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`*-commutative`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `pow-plus` `cube-unmult` `pow-sqr` `flip-+` `unswap-sqr`

Counts

3 → 59

Calls

3 calls:

Slowest

44.0ms	(* (* x (* x x)) -2/3)
21.0ms	(* x (* x x))
9.0ms	(+ (* x x) (* (* x (* x x)) -2/3))

series216.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

116.0ms	(+ (* x x) (* (* x (* x x)) -2/3))
53.0ms	(* (* x (* x x)) -2/3)
47.0ms	(* x (* x x))

simplify3.7s

Counts

35 → 68

Calls

35 calls:

Slowest

532.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
413.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
360.0ms	(* (* (* (* x (* x x)) (* x (* x x))) (* x (* x x))) (* (* -2/3 -2/3) -2/3))
358.0ms	(* (exp (* x x)) (exp (* (* x (* x x)) -2/3)))
313.0ms	(* (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x))) (* (* -2/3 -2/3) -2/3))

prune667.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize64.0ms

Local error

Found 4 expressions with local error:

30.2b	(posit16->real (real->posit16 (* (* x (* x x)) -2/3)))
6.6b	(- (- 2 (* x x)) (posit16->real (real->posit16 (* (* x (* x x)) -2/3))))
0.1b	(* (* x (* x x)) -2/3)
0.1b	(* x (* x x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt`
5×	`pow-prod-up`
4×	`associate-r` `associate-l` `insert-posit16`
3×	`diff-log`
2×	`sub-neg` `associate--l+` `*-commutative`
1×	`associate--l-` `pow2` `pow-plus` `flip3--` `cube-unmult` `pow-sqr` `remove-posit16` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

Slowest

69.0ms	(* (* x (* x x)) -2/3)
29.0ms	(- (- 2 (* x x)) (posit16->real (real->posit16 (* (* x (* x x)) -2/3))))
27.0ms	(* x (* x x))
0.0ms	(posit16->real (real->posit16 (* (* x (* x x)) -2/3)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

76.0ms	(posit16->real (real->posit16 (* (* x (* x x)) -2/3)))
58.0ms	(* (* x (* x x)) -2/3)
57.0ms	(- (- 2 (* x x)) (posit16->real (real->posit16 (* (* x (* x x)) -2/3))))
54.0ms	(* x (* x x))

simplify4.7s

Counts

43 → 87

Calls

43 calls:

Slowest

517.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
499.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
481.0ms	(/ (/ (exp 2) (exp (* x x))) (exp (posit16->real (real->posit16 (* (* x (* x x)) -2/3)))))
408.0ms	(* (* (* (* x (* x x)) (* x (* x x))) (* x (* x x))) (* (* -2/3 -2/3) -2/3))
284.0ms	(* (* (* (* x x) x) (* (* (* x x) x) (* (* x x) x))) (* (* -2/3 -2/3) -2/3))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes176.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.5b

bsearch390.0ms

end0.0ms

sample11.6s

Algorithm

intervals

Results

3.5s	1939×	body	10240	exit
3.3s	10043×	body	80	valid
2.6s	1721×	body	1280	valid
1.2s	1243×	body	640	valid
409.0ms	656×	body	320	valid
122.0ms	331×	body	160	valid