Details

sample284.0ms

Algorithm

intervals

Results

116.0ms	60×	body	10240	exit
51.0ms	334×	body	80	valid
46.0ms	45×	body	1280	valid
36.0ms	48×	body	640	valid
11.0ms	23×	body	320	valid
2.0ms	8×	body	160	valid

simplify237.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

236.0ms

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize55.0ms

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

rewrite597.0ms

Algorithm

rewrite-expression-head

Rules

4843×	`prod-diff`
3476×	`exp-sum`
2787×	`*-un-lft-identity`
2775×	`add-sqr-sqrt`
2749×	`add-cube-cbrt`
1977×	`associate--r+`
1954×	`times-frac`
1740×	`distribute-rgt-in` `distribute-lft-in`
318×	`sub-neg`
26×	`div-inv`
25×	`associate-/l*`
16×	`add-log-exp`
11×	`distribute-lft-out`
10×	`add-cbrt-cube` `distribute-lft-out--`
9×	`add-exp-log` `difference-of-squares`
8×	`pow1` `associate-r`
6×	`diff-log` `associate-l`
4×	`expm1-log1p-u` `flip3-+` `fma-neg` `associate-*r/` `frac-sub` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate--l+` `associate--r-`

Counts

4 → 2204

Calls

4 calls:

Slowest

240.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
28.0ms	(/ (exp (* x (- -1 eps))) eps)
26.0ms	(* x (+ -1 eps))
12.0ms	(* x (+ -1 eps))

series240.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
52.0ms	(* x (+ -1 eps))
32.0ms	(* x (+ -1 eps))
29.0ms	(/ (exp (* x (- -1 eps))) eps)

simplify7.0m

Counts

2267 → 2216

Calls

2267 calls:

Slowest

859.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
844.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
810.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
799.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
784.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))

prune26.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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))

rewrite13.0ms

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

12.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series75.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

43.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
32.0ms	(* x (* x x))

simplify1.1s

Counts

20 → 44

Calls

20 calls:

Slowest

316.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
310.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
128.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
126.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
126.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune256.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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

12.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series70.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

37.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
32.0ms	(* x (* x x))

simplify1.1s

Counts

20 → 44

Calls

20 calls:

Slowest

316.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
309.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
127.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
127.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
126.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune246.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

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)))
3.6b	(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)))))

rewrite11.0ms

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

9.0ms	(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)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

38.0ms	(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)))))
38.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
33.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
32.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify1.7s

Counts

14 → 58

Calls

14 calls:

Slowest

129.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
129.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
128.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
128.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
127.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune372.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes98.0ms

Accuracy

96.6% (0.5b remaining)

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

bsearch229.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.7s	1939×	body	10240	exit
1.9s	1721×	body	1280	valid
1.5s	10043×	body	80	valid
794.0ms	1243×	body	640	valid
541.0ms	656×	body	320	valid
80.0ms	331×	body	160	valid