Details

sample80.0ms

Algorithm

intervals

Results

35.0ms	74×	body	1280	valid
18.0ms	54×	body	640	valid
12.0ms	158×	body	80	valid
5.0ms	24×	body	320	valid
2.0ms	16×	body	160	valid

simplify19.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

19.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize15.0ms

Local error

Found 2 expressions with local error:

4.5b	(- (exp x) 1)
0.0b	(/ (- (exp x) 1) x)

rewrite59.0ms

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-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

Slowest

41.0ms	(/ (- (exp x) 1) x)
16.0ms	(- (exp x) 1)

series74.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

59.0ms	(/ (- (exp x) 1) x)
15.0ms	(- (exp x) 1)

simplify1.9s

Counts

67 → 70

Calls

67 calls:

Slowest

254.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
239.0ms	(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
114.0ms	(* -1 (/ (- 1 (exp x)) x))
59.0ms	(- (pow (exp x) 3) (pow 1 3))
59.0ms	(/ (- (sqrt (exp x)) (sqrt 1)) (sqrt x))

prune473.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.4b	(* 1/6 x)
0.1b	(* x (+ (* 1/6 x) 1/2))
0.0b	(+ (* 1/6 x) 1/2)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

Slowest

21.0ms	(* x (+ (* 1/6 x) 1/2))
10.0ms	(* 1/6 x)
6.0ms	(+ (* 1/6 x) 1/2)

series135.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

71.0ms	(* x (+ (* 1/6 x) 1/2))
41.0ms	(+ (* 1/6 x) 1/2)
23.0ms	(* 1/6 x)

simplify1.1s

Counts

33 → 63

Calls

33 calls:

Slowest

271.0ms	(+ (* (* 1/6 x) (* 1/6 x)) (- (* 1/2 1/2) (* (* 1/6 x) 1/2)))
215.0ms	(* (* (* x x) x) (* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2)))
188.0ms	(* (* (* 1/6 1/6) 1/6) (* (* x x) x))
56.0ms	(* (exp (* 1/6 x)) (exp 1/2))
50.0ms	(+ (* 1/2 x) (* 1/6 (pow x 2)))

prune413.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (exp x) 1)
4.5b	(- (exp x) 1)
4.5b	(- (exp x) 1)
0.1b	(cbrt (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
16×	`add-sqr-sqrt`
14×	`associate-*l/`
13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`associate-*r/`
6×	`difference-of-squares`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`sub-neg` `diff-log` `difference-of-sqr-1` `distribute-lft-out--`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 88

Calls

4 calls:

Slowest

81.0ms	(cbrt (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
20.0ms	(- (exp x) 1)
16.0ms	(- (exp x) 1)
13.0ms	(- (exp x) 1)

series77.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

25.0ms	(cbrt (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
19.0ms	(- (exp x) 1)
19.0ms	(- (exp x) 1)
15.0ms	(- (exp x) 1)

simplify7.3s

Counts

61 → 100

Calls

61 calls:

Slowest

674.0ms	(cbrt (* (* (- (* (exp x) (exp x)) (* 1 1)) (- (* (exp x) (exp x)) (* 1 1))) (- (exp x) 1)))
382.0ms	(cbrt (* (* (- (exp x) 1) (- (exp x) 1)) (- (* (exp x) (exp x)) (* 1 1))))
338.0ms	(cbrt (* (* (- (pow (exp x) 3) (pow 1 3)) (- (pow (exp x) 3) (pow 1 3))) (- (pow (exp x) 3) (pow 1 3))))
319.0ms	(cbrt (* (* (- (* (exp x) (exp x)) (* 1 1)) (- (exp x) 1)) (- (pow (exp x) 3) (pow 1 3))))
305.0ms	(cbrt (* (* (- (exp x) 1) (- (* (exp x) (exp x)) (* 1 1))) (- (pow (exp x) 3) (pow 1 3))))

prune804.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (exp x) 1)
4.5b	(- (exp x) 1)
4.5b	(- (exp (+ (+ x x) x)) 1)
0.1b	(cbrt (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp (+ (+ x x) x)) 1)))

rewrite841.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
16×	`add-sqr-sqrt`
14×	`associate-*l/`
13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`associate-*r/`
6×	`difference-of-squares`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`sub-neg` `diff-log` `difference-of-sqr-1` `distribute-lft-out--`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 87

Calls

4 calls:

Slowest

584.0ms	(- (exp (+ (+ x x) x)) 1)
225.0ms	(cbrt (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp (+ (+ x x) x)) 1)))
17.0ms	(- (exp x) 1)
14.0ms	(- (exp x) 1)

series279.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(cbrt (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp (+ (+ x x) x)) 1)))
34.0ms	(- (exp (+ (+ x x) x)) 1)
15.0ms	(- (exp x) 1)
15.0ms	(- (exp x) 1)

simplify10.0s

Counts

60 → 99

Calls

60 calls:

Slowest

516.0ms	(cbrt (* (* (- (pow (exp x) 3) (pow 1 3)) (- (pow (exp x) 3) (pow 1 3))) (- (exp (+ (+ x x) x)) 1)))
486.0ms	(cbrt (* (* (- (pow (exp x) 3) (pow 1 3)) (- (exp x) 1)) (- (pow (exp (+ (+ x x) x)) 3) (pow 1 3))))
461.0ms	(cbrt (* (* (- (* (exp x) (exp x)) (* 1 1)) (- (exp x) 1)) (- (pow (exp (+ (+ x x) x)) 3) (pow 1 3))))
430.0ms	(cbrt (* (* (- (pow (exp x) 3) (pow 1 3)) (- (* (exp x) (exp x)) (* 1 1))) (- (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* 1 1))))
429.0ms	(cbrt (* (* (- (exp x) 1) (- (* (exp x) (exp x)) (* 1 1))) (- (pow (exp (+ (+ x x) x)) 3) (pow 1 3))))

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 20.9b

bsearch61.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	2327×	body	1280	valid
575.0ms	1670×	body	640	valid
398.0ms	5240×	body	80	valid
192.0ms	815×	body	320	valid
54.0ms	395×	body	160	valid