Details

sample121.0ms

Algorithm

intervals

Results

44.0ms	74×	body	1280	valid
35.0ms	91×	body	10240	exit
18.0ms	59×	body	640	valid
6.0ms	88×	body	80	valid
5.0ms	22×	body	320	valid
2.0ms	13×	body	160	valid

simplify19.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

18.0ms

(/ (exp x) (- (exp x) 1))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize8.0ms

Local error

Found 2 expressions with local error:

4.5b	(- (exp x) 1)
1.2b	(/ (exp x) (- (exp x) 1))

rewrite26.0ms

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

15.0ms	(/ (exp x) (- (exp x) 1))
9.0ms	(- (exp x) 1)

series58.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

31.0ms	(- (exp x) 1)
27.0ms	(/ (exp x) (- (exp x) 1))

simplify2.3s

Counts

88 → 86

Calls

88 calls:

Slowest

256.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
226.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
90.0ms	(fma (* (cbrt (exp x)) (cbrt (exp x))) (cbrt (exp x)) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))
83.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))
81.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (sqrt 1) (sqrt 1))))

prune523.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-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` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `fma-udef` `div-inv`

Counts

2 → 30

Calls

2 calls:

Slowest

6.0ms	(+ 1/2 (/ 1 x))
0.0ms	(fma x 1/12 (+ 1/2 (/ 1 x)))

series36.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

23.0ms	(fma x 1/12 (+ 1/2 (/ 1 x)))
14.0ms	(+ 1/2 (/ 1 x))

simplify225.0ms

Counts

11 → 36

Calls

11 calls:

Slowest

46.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
43.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
25.0ms	(* (exp 1/2) (exp (/ 1 x)))
24.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
17.0ms	(+ (/ 1 x) 1/2)

prune275.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`fma-def`
12×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
4×	`add-log-exp`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `fma-udef`

Counts

2 → 40

Calls

2 calls:

Slowest

13.0ms	(+ (/ 1 x) 1/2)
0.0ms	(fma x 1/12 (+ (/ 1 x) 1/2))

series45.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

24.0ms	(+ (/ 1 x) 1/2)
21.0ms	(fma x 1/12 (+ (/ 1 x) 1/2))

simplify384.0ms

Counts

20 → 46

Calls

20 calls:

Slowest

46.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
46.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
43.0ms	(/ (* (cbrt 1) (cbrt 1)) (* (cbrt x) (cbrt x)))
35.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
25.0ms	(* (exp (/ 1 x)) (exp 1/2))

prune322.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

localize26.0ms

Local error

Found 4 expressions with local error:

28.3b	(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
1.2b	(/ (exp x) (expm1 x))
1.2b	(/ (exp x) (expm1 x))
1.2b	(/ (exp x) (expm1 x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`add-cbrt-cube`
9×	`associate-/r` `associate-/l`
7×	`cbrt-div` `add-exp-log`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-*l/` `div-inv`
1×	`cbrt-prod` `pow1/3` `cube-unmult` `rem-cbrt-cube`

Counts

4 → 110

Calls

4 calls:

Slowest

49.0ms	(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))
11.0ms	(/ (exp x) (expm1 x))
9.0ms	(/ (exp x) (expm1 x))
6.0ms	(/ (exp x) (expm1 x))

series153.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

46.0ms	(/ (exp x) (expm1 x))
39.0ms	(/ (exp x) (expm1 x))
39.0ms	(/ (exp x) (expm1 x))
28.0ms	(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (/ (exp x) (expm1 x)))))

simplify2.8s

Counts

96 → 122

Calls

96 calls:

Slowest

474.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
409.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
378.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (expm1 x) (expm1 x)) (expm1 x)))
138.0ms	(cbrt (* (/ (exp x) (expm1 x)) (* (/ (exp x) (expm1 x)) (exp x))))
126.0ms	(cbrt (* (exp x) (* (exp x) (exp x))))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.1b

regimes53.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.2b

bsearch42.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2292×	body	1280	valid
983.0ms	2604×	body	10240	exit
485.0ms	1645×	body	640	valid
201.0ms	2832×	body	80	valid
150.0ms	812×	body	320	valid
111.0ms	420×	body	160	valid