Details

sample340.0ms

Algorithm

intervals

Results

144.0ms	61×	body	10240	exit
68.0ms	61×	body	1280	valid
57.0ms	333×	body	80	valid
31.0ms	39×	body	640	valid
16.0ms	24×	body	320	valid
2.0ms	6×	body	160	valid

simplify303.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

303.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize65.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b	(exp (* x (+ -1 eps)))
0.0b	(exp (* x (+ -1 eps)))
0.0b	(exp (* x (- -1 eps)))

rewrite575.0ms

Algorithm

rewrite-expression-head

Rules

4789×	`prod-diff`
3414×	`exp-sum`
2713×	`*-un-lft-identity`
2701×	`add-sqr-sqrt`
2679×	`add-cube-cbrt`
1977×	`associate--r+`
1879×	`times-frac`
1707×	`distribute-rgt-in` `distribute-lft-in`
312×	`sub-neg`
25×	`div-inv`
22×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`distribute-lft-out` `difference-of-squares`
6×	`diff-log`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `flip3--` `exp-to-pow` `flip--` `rem-exp-log`
2×	`sum-log` `flip3-+` `flip-+`
1×	`associate--l+` `associate--r-`

Counts

4 → 2099

Calls

4 calls:

Slowest

337.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
12.0ms	(exp (* x (- -1 eps)))
5.0ms	(exp (* x (+ -1 eps)))
5.0ms	(exp (* x (+ -1 eps)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
28.0ms	(exp (* x (- -1 eps)))
18.0ms	(exp (* x (+ -1 eps)))
14.0ms	(exp (* x (+ -1 eps)))

simplify6.7m

Counts

2094 → 2111

Calls

2094 calls:

Slowest

852.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
812.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
806.0ms	(fma 1 (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (* (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))))
770.0ms	(fma (- (exp (* (fma (- (cbrt eps)) (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (* (cbrt eps) (cbrt eps)))) x))) (exp (* (fma 1 -1 (- (* (cbrt eps) (* (cbrt eps) (cbrt eps))))) x)) (* (exp (* (fma (- (cbrt eps)) (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (* (cbrt eps) (cbrt eps)))) x)) (exp (* (fma 1 -1 (- (* (cbrt eps) (* (cbrt eps) (cbrt eps))))) x))))
760.0ms	(fma (- (exp (* (fma (- (cbrt eps)) (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (* (cbrt eps) (cbrt eps)))) x))) (exp (* (fma 1 -1 (- (* (cbrt eps) (* (cbrt eps) (cbrt eps))))) x)) (* (exp (* (fma (- (cbrt eps)) (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (* (cbrt eps) (cbrt eps)))) x)) (exp (* (fma 1 -1 (- (* (cbrt eps) (* (cbrt eps) (cbrt eps))))) x))))

prune32.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

7.6b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
0.1b	(* x (* x x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

Slowest

13.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

34.0ms	(* x (* x x))
33.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify1.0s

Counts

20 → 44

Calls

20 calls:

Slowest

303.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
300.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
124.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
123.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
121.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune223.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.0b

bsearch231.0ms

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.3s	1866×	body	10240	exit
1.5s	1728×	body	1280	valid
1.4s	10035×	body	80	valid
1.0s	1238×	body	640	valid
268.0ms	618×	body	320	valid
67.0ms	312×	body	160	valid