Details

sample99.0ms

Algorithm

intervals

Results

29.0ms	63×	body	1280	valid
26.0ms	66×	body	10240	exit
21.0ms	62×	body	640	valid
7.0ms	28×	body	320	valid
6.0ms	94×	body	80	valid
1.0ms	9×	body	160	valid

simplify10.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

10.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize9.0ms

Local error

Found 2 expressions with local error:

2.9b	(- (exp x) 1)
0.5b	(/ (exp x) (- (exp x) 1))

rewrite42.0ms

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

26.0ms	(- (exp x) 1)
14.0ms	(/ (exp x) (- (exp x) 1))

series57.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

30.0ms	(/ (exp x) (- (exp x) 1))
27.0ms	(- (exp x) 1)

simplify1.8s

Counts

68 → 69

Calls

68 calls:

Slowest

448.0ms	(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
217.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
76.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
64.0ms	(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
41.0ms	(/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (sqrt (exp x)) 1))

prune526.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

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)

rewrite52.0ms

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

30.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
17.0ms	(+ (/ 1 x) 1/2)
5.0ms	(* 1/12 x)

series49.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

17.0ms	(+ (/ 1 x) 1/2)
16.0ms	(* 1/12 x)
15.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

simplify1.2s

Counts

23 → 56

Calls

23 calls:

Slowest

377.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
367.0ms	(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
197.0ms	(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
35.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
30.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune408.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize16.0ms

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)

rewrite45.0ms

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

23.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
16.0ms	(+ (/ 1 x) 1/2)
5.0ms	(* 1/12 x)

series80.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

31.0ms	(* 1/12 x)
25.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
23.0ms	(+ (/ 1 x) 1/2)

simplify1.1s

Counts

23 → 56

Calls

23 calls:

Slowest

410.0ms	(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
372.0ms	(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
126.0ms	(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
43.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
43.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune374.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (* (exp x) (exp x)) (* 1 1))
0.5b	(/ (exp x) (- (* (exp x) (exp x)) (* 1 1)))
0.5b	(* (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))) (+ (exp x) 1))
0.0b	(+ (exp x) 1)

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

Slowest

118.0ms	(* (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))) (+ (exp x) 1))
27.0ms	(/ (exp x) (- (* (exp x) (exp x)) (* 1 1)))
13.0ms	(- (* (exp x) (exp x)) (* 1 1))
12.0ms	(+ (exp x) 1)

series191.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(* (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))) (+ (exp x) 1))
69.0ms	(/ (exp x) (- (* (exp x) (exp x)) (* 1 1)))
27.0ms	(- (* (exp x) (exp x)) (* 1 1))
13.0ms	(+ (exp x) 1)

simplify9.7s

Counts

90 → 118

Calls

90 calls:

Slowest

687.0ms	(/ (* (exp x) (+ (exp x) 1)) (- (pow (exp x) 2) 1))
679.0ms	(/ (* (exp x) (+ (exp x) 1)) (- (pow (exp x) 2) 1))
416.0ms	(* (- (* (exp x) (exp x)) (* 1 1)) (- (exp x) 1))
415.0ms	(* 1 (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))))
374.0ms	(* (/ (exp x) (- (* (exp x) (exp x)) (* 1 1))) (+ (exp x) 1))

prune934.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes167.0ms

Accuracy

97.9% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 21.2b

bsearch6.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2560×	body	10240	exit
1.0s	2285×	body	1280	valid
542.0ms	1668×	body	640	valid
230.0ms	827×	body	320	valid
230.0ms	2841×	body	80	valid
71.0ms	380×	body	160	valid