Details

sample356.0ms

Algorithm

intervals

Results

134.0ms	55×	body	1280	valid
86.0ms	65×	body	10240	exit
61.0ms	344×	body	80	valid
30.0ms	40×	body	640	valid
10.0ms	17×	body	320	valid
2.0ms	4×	body	160	valid

simplify685.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

685.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite644.0ms

Algorithm

rewrite-expression-head

Rules

4861×	`prod-diff`
3506×	`exp-sum`
2801×	`*-un-lft-identity`
2789×	`add-sqr-sqrt`
2767×	`add-cube-cbrt`
1977×	`associate--r+`
1969×	`times-frac`
1753×	`distribute-rgt-in` `distribute-lft-in`
320×	`sub-neg`
30×	`associate-/l*`
27×	`div-inv`
18×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`distribute-lft-out` `difference-of-squares`
8×	`add-cbrt-cube`
6×	`associate-/r*` `diff-log` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `fma-neg` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-exp` `flip-+`
1×	`exp-prod` `exp-to-pow` `associate--l+` `associate--r-` `rem-exp-log`

Counts

4 → 2225

Calls

4 calls:

Slowest

348.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
14.0ms	(/ (exp (* x (- -1 eps))) eps)
9.0ms	(/ (exp (* x (+ -1 eps))) eps)
9.0ms	(exp (* x (- -1 eps)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

144.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
44.0ms	(/ (exp (* x (- -1 eps))) eps)
43.0ms	(/ (exp (* x (+ -1 eps))) eps)
24.0ms	(exp (* x (- -1 eps)))

simplify8.1m

Counts

2300 → 2237

Calls

2300 calls:

Slowest

855.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
834.0ms	(fma (- (exp (* x (fma (- (cbrt eps)) (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (* (cbrt eps) (cbrt eps))))))) (exp (* x (fma 1 -1 (- (* (cbrt eps) (* (cbrt eps) (cbrt eps))))))) (* (exp (* x (fma (- (cbrt eps)) (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (* (cbrt eps) (cbrt eps)))))) (exp (* x (fma 1 -1 (- (* (cbrt eps) (* (cbrt eps) (cbrt eps)))))))))
830.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
813.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
780.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))

prune28.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 2 expressions with local error:

6.7b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
0.1b	(* x (* x x))

rewrite19.0ms

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

18.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series71.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

35.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
35.0ms	(* x (* x x))

simplify1.2s

Counts

20 → 44

Calls

20 calls:

Slowest

346.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
341.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
143.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
141.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
141.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune288.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize22.0ms

Local error

Found 4 expressions with local error:

6.7b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
6.7b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
6.7b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
5.4b	(cbrt (* (* (fma (* x (* x x)) 2/3 (- 2 (* x x))) (fma (* x (* x x)) 2/3 (- 2 (* x x)))) (fma (* x (* x x)) 2/3 (- 2 (* x x)))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 46

Calls

4 calls:

Slowest

16.0ms	(cbrt (* (* (fma (* x (* x x)) 2/3 (- 2 (* x x))) (fma (* x (* x x)) 2/3 (- 2 (* x x)))) (fma (* x (* x x)) 2/3 (- 2 (* x x)))))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

41.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
39.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
35.0ms	(cbrt (* (* (fma (* x (* x x)) 2/3 (- 2 (* x x))) (fma (* x (* x x)) 2/3 (- 2 (* x x)))) (fma (* x (* x x)) 2/3 (- 2 (* x x)))))
35.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify1.8s

Counts

14 → 58

Calls

14 calls:

Slowest

143.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
143.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
142.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
142.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
142.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune452.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 2 expressions with local error:

6.7b	(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)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

42.0ms	(* x (* x x))
35.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify1.2s

Counts

20 → 44

Calls

20 calls:

Slowest

347.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
341.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
142.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
139.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
136.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune257.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

regimes123.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.8b

bsearch201.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

3.1s	1986×	body	10240	exit
1.9s	1680×	body	1280	valid
1.7s	10180×	body	80	valid
850.0ms	1294×	body	640	valid
252.0ms	615×	body	320	valid
76.0ms	313×	body	160	valid