Details

sample75.0ms

Algorithm

intervals

Results

26.0ms	96×	body	10240	exit
21.0ms	66×	body	1280	valid
9.0ms	42×	body	640	valid
5.0ms	105×	body	80	valid
5.0ms	34×	body	320	valid
1.0ms	10×	body	160	valid

simplify10.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

10.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize7.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (exp x) 1)
0.0b	(/ (exp x) (- (exp x) 1))

rewrite44.0ms

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

33.0ms	(/ (exp x) (- (exp x) 1))
10.0ms	(- (exp x) 1)

series64.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

44.0ms	(/ (exp x) (- (exp x) 1))
20.0ms	(- (exp x) 1)

simplify2.0s

Counts

68 → 69

Calls

68 calls:

Slowest

462.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
237.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
81.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
58.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
43.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune586.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

Slowest

45.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
19.0ms	(+ (/ 1 x) 1/2)
10.0ms	(* 1/12 x)

series77.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

27.0ms	(* 1/12 x)
26.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
23.0ms	(+ (/ 1 x) 1/2)

simplify1.2s

Counts

23 → 56

Calls

23 calls:

Slowest

385.0ms	(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
334.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
249.0ms	(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
45.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
43.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune336.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.5b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.5b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.4b	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

rewrite269.0ms

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

165.0ms	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
35.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
34.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
34.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
111.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
104.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
77.0ms	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))

simplify10.2s

Counts

83 → 103

Calls

83 calls:

Slowest

549.0ms	(* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
500.0ms	(+ (* 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))))))))
448.0ms	(* (+ (* 1/12 x) (+ (/ 1 x) 1/2)) (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
430.0ms	(- (+ (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))))
407.0ms	(- (+ (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))))

prune979.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

3.1b	(- (* (exp x) (exp x)) (* 1 1))
0.0b	(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
0.0b	(* (exp x) (exp x))
0.0b	(+ (exp x) 1)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`exp-prod`
16×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `distribute-lft-out` `difference-of-squares`
4×	`associate-/r` `pow-prod-down` `pow-sqr` `pow-prod-up` `insert-posit16` `associate-/l`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

Slowest

51.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
14.0ms	(- (* (exp x) (exp x)) (* 1 1))
12.0ms	(* (exp x) (exp x))
6.0ms	(+ (exp x) 1)

series130.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

61.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (+ (exp x) 1))
36.0ms	(- (* (exp x) (exp x)) (* 1 1))
23.0ms	(* (exp x) (exp x))
10.0ms	(+ (exp x) 1)

simplify6.2s

Counts

101 → 116

Calls

101 calls:

Slowest

680.0ms	(/ (* (* (- (* (exp x) (exp x)) (* 1 1)) (- (* (exp x) (exp x)) (* 1 1))) (- (* (exp x) (exp x)) (* 1 1))) (* (* (+ (exp x) 1) (+ (exp x) 1)) (+ (exp x) 1)))
406.0ms	(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
297.0ms	(/ (- (pow (exp x) 2) 1) (+ (exp x) 1))
297.0ms	(+ (* 2 x) (+ (* 4/3 (pow x 3)) (* 2 (pow x 2))))
278.0ms	(- (pow (* (exp x) (exp x)) 3) (pow (* 1 1) 3))

prune878.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes145.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 21.1b

bsearch41.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	2598×	body	10240	exit
964.0ms	2326×	body	1280	valid
518.0ms	1654×	body	640	valid
225.0ms	805×	body	320	valid
172.0ms	2811×	body	80	valid
46.0ms	405×	body	160	valid