Details

sample80.0ms

Algorithm

intervals

Results

21.0ms	78×	body	1280	valid
20.0ms	96×	body	10240	exit
16.0ms	35×	body	640	valid
4.0ms	100×	body	80	valid
3.0ms	29×	body	320	valid
1.0ms	14×	body	160	valid

simplify15.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
4.0b	(- (exp x) 1.0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1.0))
18.0ms	(- (exp x) 1.0)

series80.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (exp x) (- (exp x) 1.0))
24.0ms	(- (exp x) 1.0)

simplify744.0ms

Counts: 57 → 57

prune523.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

24.0ms	(+ (* 1/12 x) (/ 1 x))
7.0ms	(* 1/12 x)

series66.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(+ (* 1/12 x) (/ 1 x))
16.0ms	(* 1/12 x)

simplify1000.0ms

Counts: 35 → 35

prune90.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
4.0b	(- 1 (/ 1.0 (exp x)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
43×	`times-frac`
24×	`add-cube-cbrt`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`div-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--` `div-inv`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 97

Calls

3 calls:

65.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
14.0ms	(/ 1.0 (exp x))
40.0ms	(- 1 (/ 1.0 (exp x)))

series130.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
22.0ms	(/ 1.0 (exp x))
44.0ms	(- 1 (/ 1.0 (exp x)))

simplify1.4s

Counts: 106 → 106

prune226.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (pow x 2) (- (* x 0.16666666666666666) 0.5)) (* 1.0 x))
0.1b	(* (pow x 2) (- (* x 0.16666666666666666) 0.5))
0.3b	(/ 1 (+ (* (pow x 2) (- (* x 0.16666666666666666) 0.5)) (* 1.0 x)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log`
9×	`times-frac`
8×	`associate-l`
7×	`add-cbrt-cube`
5×	`add-log-exp`
4×	`pow1` `distribute-rgt-in` `sub-neg` `unpow-prod-down` `associate-+l+` `distribute-lft-in` `unswap-sqr`
3×	`associate-r` `prod-exp` `associate-/r` `associate-/l`
2×	`flip3-+` `associate-*r/` `div-exp` `associate-/r/` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `1-exp` `pow-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `inv-pow`

Counts

3 → 81

Calls

3 calls:

43.0ms	(+ (* (pow x 2) (- (* x 0.16666666666666666) 0.5)) (* 1.0 x))
74.0ms	(* (pow x 2) (- (* x 0.16666666666666666) 0.5))
69.0ms	(/ 1 (+ (* (pow x 2) (- (* x 0.16666666666666666) 0.5)) (* 1.0 x)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ (* (pow x 2) (- (* x 0.16666666666666666) 0.5)) (* 1.0 x))
123.0ms	(* (pow x 2) (- (* x 0.16666666666666666) 0.5))
72.0ms	(/ 1 (+ (* (pow x 2) (- (* x 0.16666666666666666) 0.5)) (* 1.0 x)))

simplify790.0ms

Counts: 90 → 90

prune256.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

91.1% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 7.3b

bsearch3.0ms

simplify2.4s

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	2650×	body	10240	exit
661.0ms	2277×	body	1280	valid
323.0ms	1638×	body	640	valid
160.0ms	2844×	body	80	valid
94.0ms	817×	body	320	valid
32.0ms	425×	body	160	valid