Details

sample46.0ms

Algorithm

intervals

Results

12.0ms	63×	body	1280	valid
11.0ms	83×	body	10240	exit
7.0ms	62×	body	640	valid
3.0ms	33×	body	320	valid
2.0ms	86×	body	80	valid
1.0ms	12×	body	160	valid

simplify14.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
4.6b	(- (exp x) 1.0)

rewrite50.0ms

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:

37.0ms	(/ (exp x) (- (exp x) 1.0))
11.0ms	(- (exp x) 1.0)

series51.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1.0))
20.0ms	(- (exp x) 1.0)

simplify676.0ms

Counts: 57 → 57

prune169.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

26.0ms	(+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)
32.0ms	(/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
24.0ms	(* (pow x 2) (+ 1/2 (* 1/6 x)))
12.0ms	(* 1/6 x)

series212.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)
52.0ms	(/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
88.0ms	(* (pow x 2) (+ 1/2 (* 1/6 x)))
26.0ms	(* 1/6 x)

simplify1.1s

Counts: 103 → 103

prune372.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))) (cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))))
0.4b	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
0.4b	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
0.4b	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

117×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
18×	`swap-sqr` `associate-r` `associate-l`
14×	`associate-/r/`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `flip3-+` `flip-+` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

152.0ms	(* (cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))) (cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))))
24.0ms	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
25.0ms	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
27.0ms	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))) (cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))))
154.0ms	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
141.0ms	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
147.0ms	(cbrt (/ (exp x) (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))

simplify948.0ms

Counts: 168 → 168

prune919.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

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:

21.0ms	(+ (* 1/12 x) (/ 1 x))
18.0ms	(* 1/12 x)

series82.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ (* 1/12 x) (/ 1 x))
15.0ms	(* 1/12 x)

simplify1.1s

Counts: 35 → 35

prune87.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

63% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 1.1b

bsearch2.0ms

simplify1.1s

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	2244×	body	1280	valid
804.0ms	2617×	body	10240	exit
303.0ms	1659×	body	640	valid
148.0ms	2830×	body	80	valid
136.0ms	798×	body	320	valid
35.0ms	470×	body	160	valid