Details

sample314.0ms

Algorithm

intervals

Results

118.0ms	58×	body	10240	exit
65.0ms	54×	body	1280	valid
57.0ms	312×	body	80	valid
36.0ms	47×	body	640	valid
10.0ms	21×	body	320	valid
2.0ms	8×	body	160	valid

simplify1.9s

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize34.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ (- (exp (* x (- -1 eps))) (/ (exp (* x (- -1 eps))) eps)) (+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x))))
0.0b	(+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x)))
0.0b	(- (* x eps) x)
0.0b	(- (* x eps) x)

rewrite900.0ms

Algorithm

rewrite-expression-head

Rules

4762×	`prod-diff`
3403×	`exp-sum`
2690×	`*-un-lft-identity`
2679×	`add-sqr-sqrt`
2674×	`add-cube-cbrt`
1977×	`associate-+l+`
1900×	`times-frac`
1694×	`distribute-rgt-in` `distribute-lft-in`
314×	`sub-neg`
34×	`fma-def`
26×	`div-inv`
22×	`add-log-exp`
9×	`frac-add`
7×	`sum-log` `distribute-lft-out`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `flip3-+` `add-cbrt-cube` `diff-log` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`exp-diff` `distribute-lft-out--`
2×	`+-commutative` `fma-neg` `difference-of-squares`
1×	`associate-+r+` `associate-+l-`

Counts

4 → 2094

Calls

4 calls:

Slowest

559.0ms	(+ (- (exp (* x (- -1 eps))) (/ (exp (* x (- -1 eps))) eps)) (+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x))))
86.0ms	(+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x)))
8.0ms	(- (* x eps) x)
8.0ms	(- (* x eps) x)

series324.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(+ (- (exp (* x (- -1 eps))) (/ (exp (* x (- -1 eps))) eps)) (+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x))))
63.0ms	(- (* x eps) x)
60.0ms	(- (* x eps) x)
43.0ms	(+ (/ (exp (- (* x eps) x)) eps) (exp (- (* x eps) x)))

simplify3.1s

Counts: 2106 → 2106

prune44.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 3 expressions with local error:

6.6b	(- (fma 2/3 (* x (* x x)) 2) (* x x))
0.1b	(* x (* x x))
0.0b	(fma 2/3 (* x (* x x)) 2)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
8×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow-prod-up` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
2×	`fma-udef`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `cube-unmult` `associate-r` `associate--l+` `pow-sqr` `*-commutative` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

Slowest

20.0ms	(* x (* x x))
6.0ms	(- (fma 2/3 (* x (* x x)) 2) (* x x))
0.0ms	(fma 2/3 (* x (* x x)) 2)

series211.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

115.0ms	(fma 2/3 (* x (* x x)) 2)
50.0ms	(- (fma 2/3 (* x (* x x)) 2) (* x x))
46.0ms	(* x (* x x))

simplify694.0ms

Counts: 70 → 70

prune567.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite120.0ms

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`
7×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-+r+` `pow-prod-up`
3×	`expm1-log1p-u` `prod-diff` `insert-posit16` `log1p-expm1-u`
2×	`sum-log` `associate-r` `*-commutative`
1×	`pow2` `+-commutative` `associate-+r-` `sub-neg` `fma-def` `flip3-+` `pow-plus` `diff-log` `cube-unmult` `pow-sqr` `flip-+` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

Slowest

55.0ms	(* 2/3 (* x (* x x)))
42.0ms	(+ (* 2/3 (* x (* x x))) (- 2 (* x x)))
22.0ms	(* x (* x x))

series119.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

45.0ms	(* 2/3 (* x (* x x)))
37.0ms	(* x (* x x))
36.0ms	(+ (* 2/3 (* x (* x x))) (- 2 (* x x)))

simplify957.0ms

Counts: 82 → 82

prune735.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

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

28.0ms	(* x (* x x))
1.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series211.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

141.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
70.0ms	(* x (* x x))

simplify2.5s

Counts: 44 → 44

prune408.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes158.0ms

Accuracy

97.1% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.7b

bsearch360.0ms

end0.0ms

sample12.4s

Algorithm

intervals

Results

4.0s	1940×	body	10240	exit
3.0s	1765×	body	1280	valid
2.3s	10072×	body	80	valid
1.3s	1280×	body	640	valid
1.3s	610×	body	320	valid
120.0ms	306×	body	160	valid