Details

sample102.0ms

Algorithm

intervals

Results

30.0ms	84×	body	10240	exit
25.0ms	65×	body	1280	valid
23.0ms	62×	body	640	valid
6.0ms	96×	body	80	valid
3.0ms	15×	body	320	valid
3.0ms	18×	body	160	valid

simplify11.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize10.0ms

Local error

Found 2 expressions with local error:

3.9b	(- (exp x) 1)
0.3b	(/ (exp x) (- (exp x) 1))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
21×	`times-frac` `add-cube-cbrt`
10×	`difference-of-squares`
9×	`prod-diff`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`cbrt-undiv` `expm1-def` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 80

Calls

2 calls:

Slowest

45.0ms	(/ (exp x) (- (exp x) 1))
13.0ms	(- (exp x) 1)

series50.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

34.0ms	(/ (exp x) (- (exp x) 1))
16.0ms	(- (exp x) 1)

simplify705.0ms

Counts: 86 → 86

prune714.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (exp x) (expm1 (+ x (+ x x))))
0.4b	(* (/ (exp x) (expm1 (+ x (+ x x)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
0.0b	(* (exp x) (exp x))
0.0b	(expm1 (+ x (+ x x)))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
18×	`exp-prod`
16×	`associate-l`
13×	`pow1` `add-cbrt-cube`
9×	`add-exp-log`
6×	`associate-r`
5×	`pow-prod-down` `log1p-expm1-u`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`associate-/r` `swap-sqr` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `flip3-+` `div-exp` `associate-r/` `-commutative` `flip-+` `div-inv`
1×	`pow2` `distribute-rgt-in` `expm1-log1p` `clear-num` `frac-2neg` `distribute-lft-in` `pow-plus` `associate-*l/` `expm1-udef`

Counts

4 → 120

Calls

4 calls:

Slowest

226.0ms	(* (/ (exp x) (expm1 (+ x (+ x x)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
27.0ms	(* (exp x) (exp x))
11.0ms	(/ (exp x) (expm1 (+ x (+ x x))))
1.0ms	(expm1 (+ x (+ x x)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(* (/ (exp x) (expm1 (+ x (+ x x)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
36.0ms	(/ (exp x) (expm1 (+ x (+ x x))))
23.0ms	(expm1 (+ x (+ x x)))
23.0ms	(* (exp x) (exp x))

simplify818.0ms

Counts: 132 → 132

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 1/12 x (/ 1 x))
0.0b	(+ 1/2 (fma 1/12 x (/ 1 x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `associate-+r+` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

2 → 30

Calls

2 calls:

Slowest

4.0ms	(+ 1/2 (fma 1/12 x (/ 1 x)))
0.0ms	(fma 1/12 x (/ 1 x))

series115.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

92.0ms	(fma 1/12 x (/ 1 x))
23.0ms	(+ 1/2 (fma 1/12 x (/ 1 x)))

simplify2.8s

Counts: 36 → 36

prune329.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 3 expressions with local error:

1.9b	(expm1 (log1p (fma 1/12 x (/ 1 x))))
0.1b	(fma 1/12 x (/ 1 x))
0.0b	(+ 1/2 (expm1 (log1p (fma 1/12 x (/ 1 x)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`expm1-udef`
1×	`+-commutative` `expm1-log1p` `associate-+r-` `sum-log` `flip3-+` `flip-+` `fma-udef` `distribute-lft-out`

Counts

3 → 42

Calls

3 calls:

Slowest

4.0ms	(+ 1/2 (expm1 (log1p (fma 1/12 x (/ 1 x)))))
0.0ms	(expm1 (log1p (fma 1/12 x (/ 1 x))))
0.0ms	(fma 1/12 x (/ 1 x))

series205.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

73.0ms	(expm1 (log1p (fma 1/12 x (/ 1 x))))
70.0ms	(fma 1/12 x (/ 1 x))
61.0ms	(+ 1/2 (expm1 (log1p (fma 1/12 x (/ 1 x)))))

simplify883.0ms

Counts: 51 → 51

prune415.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes44.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch6.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	2552×	body	10240	exit
1.1s	2317×	body	1280	valid
566.0ms	1643×	body	640	valid
197.0ms	2793×	body	80	valid
169.0ms	814×	body	320	valid
57.0ms	436×	body	160	valid