Details

sample93.0ms

Algorithm

intervals

Results

34.0ms	81×	body	1280	valid
26.0ms	76×	body	10240	exit
13.0ms	44×	body	640	valid
6.0ms	100×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify35.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

35.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize17.0ms

Local error

Found 2 expressions with local error:

3.1b	(- (exp x) 1)
0.3b	(/ (exp x) (- (exp x) 1))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

Slowest

16.0ms	(- (exp x) 1)
13.0ms	(/ (exp x) (- (exp x) 1))

series66.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

50.0ms	(/ (exp x) (- (exp x) 1))
16.0ms	(- (exp x) 1)

simplify1.9s

Counts

68 → 69

Calls

68 calls:

Slowest

428.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
239.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
82.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
76.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
37.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune512.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x 1/6)
0.1b	(* (* x x) (+ (* x 1/6) 1/2))
0.0b	(/ (exp x) (+ x (* (* x x) (+ (* x 1/6) 1/2))))
0.0b	(+ (* x 1/6) 1/2)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log`
11×	`pow1`
9×	`times-frac`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`associate-r/` `associate-/r/` `-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `div-exp` `div-inv`

Counts

4 → 85

Calls

4 calls:

Slowest

55.0ms	(* (* x x) (+ (* x 1/6) 1/2))
17.0ms	(/ (exp x) (+ x (* (* x x) (+ (* x 1/6) 1/2))))
12.0ms	(+ (* x 1/6) 1/2)
11.0ms	(* x 1/6)

series238.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

115.0ms	(* (* x x) (+ (* x 1/6) 1/2))
48.0ms	(+ (* x 1/6) 1/2)
43.0ms	(/ (exp x) (+ x (* (* x x) (+ (* x 1/6) 1/2))))
31.0ms	(* x 1/6)

simplify7.0s

Counts

64 → 97

Calls

64 calls:

Slowest

373.0ms	(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
311.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (+ x (* (* x x) (+ (* x 1/6) 1/2))) (+ x (* (* x x) (+ (* x 1/6) 1/2)))) (+ x (* (* x x) (+ (* x 1/6) 1/2)))))
283.0ms	(+ (* x x) (- (* (* (* x x) (+ (* x 1/6) 1/2)) (* (* x x) (+ (* x 1/6) 1/2))) (* x (* (* x x) (+ (* x 1/6) 1/2)))))
272.0ms	(- x (* (* x x) (+ (* x 1/6) 1/2)))
269.0ms	(- (+ (* 18 (/ (exp x) (pow x 5))) (* 6 (/ (exp x) (pow x 3)))) (* 18 (/ (exp x) (pow x 4))))

prune961.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.3b	(* 1/12 x)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l`
2×	`insert-posit16`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

Slowest

50.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
10.0ms	(* 1/12 x)

series33.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

17.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
16.0ms	(* 1/12 x)

simplify1.0s

Counts

17 → 39

Calls

17 calls:

Slowest

384.0ms	(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
324.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
179.0ms	(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
30.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
30.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune279.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.6b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.6b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.5b	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

Slowest

223.0ms	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
30.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
20.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
20.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

87.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
80.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
76.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
74.0ms	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

simplify10.6s

Counts

83 → 103

Calls

83 calls:

Slowest

870.0ms	(* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
481.0ms	(+ (* 4 (/ (exp (* 1/3 (- (log 1/144) (* 2 (log (/ 1 x)))))) x)) (+ (* 4 (/ (exp (* 1/3 (- (log 1/144) (* 2 (log (/ 1 x)))))) (pow x 2))) (exp (* 1/3 (- (log 1/144) (* 2 (log (/ 1 x))))))))
455.0ms	(* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
451.0ms	(- (+ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) (* 2 (/ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) x))) (* 8/3 (/ (exp (* 1/3 (- (log 1/12) (log (/ 1 x))))) (pow x 3))))
412.0ms	(- (+ (exp (* 1/3 (- (log -1/12) (log (/ -1 x))))) (* 2 (/ (exp (* 1/3 (- (log -1/12) (log (/ -1 x))))) x))) (* 8/3 (/ (exp (* 1/3 (- (log -1/12) (log (/ -1 x))))) (pow x 3))))

prune881.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes164.0ms

Accuracy

73.8% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 1.1b

bsearch70.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2582×	body	10240	exit
1.1s	2237×	body	1280	valid
530.0ms	1689×	body	640	valid
163.0ms	2865×	body	80	valid
159.0ms	833×	body	320	valid
48.0ms	378×	body	160	valid