Details

sample88.0ms

Algorithm

intervals

Results

21.0ms	63×	body	1280	valid
20.0ms	54×	body	640	valid
19.0ms	74×	body	10240	exit
5.0ms	34×	body	320	valid
4.0ms	93×	body	80	valid
1.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	8	7
done	8	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (exp x) (- (exp x) 1.0))
3.8b	(- (exp x) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

35.0ms	(/ (exp x) (- (exp x) 1.0))
22.0ms	(- (exp x) 1.0)

series85.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (exp x) (- (exp x) 1.0))
39.0ms	(- (exp x) 1.0)

simplify887.0ms

Counts

73 → 73

Iterations

Useful iterations: done (884.0ms)

Iter	Nodes	Cost
0	117	900
1	254	793
2	896	708
done	5000	690

prune392.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

11.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
1.0ms	(fma 1/12 x (/ 1 x))

series137.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
109.0ms	(fma 1/12 x (/ 1 x))

simplify2.4s

Counts

34 → 34

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	41	329
1	108	314
2	360	286
3	1957	280
done	5000	279

prune217.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
3.9b	(- 1 (/ 1.0 (exp x)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
59×	`add-cube-cbrt`
39×	`prod-diff`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 145

Calls

3 calls:

14.0ms	(/ 1.0 (exp x))
68.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
46.0ms	(- 1 (/ 1.0 (exp x)))

series658.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ 1.0 (exp x))
102.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
529.0ms	(- 1 (/ 1.0 (exp x)))

simplify3.5s

Counts

154 → 154

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	257	3113
1	608	2598
2	2403	2085
done	5000	1772

prune528.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.0b	(* (/ (exp x) (- (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
0.3b	(/ (exp x) (- (pow (exp x) 3) (pow 1.0 3)))
3.8b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite679.0ms

Algorithm

rewrite-expression-head

Rules

340×	`add-sqr-sqrt`
223×	`*-un-lft-identity`
174×	`unpow-prod-down` `cube-prod`
151×	`times-frac`
144×	`prod-diff`
143×	`add-cube-cbrt`
128×	`difference-of-squares`
90×	`sqr-pow`
81×	`associate-l`
40×	`distribute-lft-out--`
26×	`cube-mult` `unpow3`
25×	`associate-/r*`
12×	`fma-neg` `add-cbrt-cube`
9×	`add-exp-log`
8×	`difference-cubes`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `associate-/r/` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod` `flip3--` `associate-r` `flip--` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `-commutative` `rem-cube-cbrt`

Counts

4 → 447

Calls

4 calls:

9.0ms	(pow (exp x) 3)
418.0ms	(* (/ (exp x) (- (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
100.0ms	(/ (exp x) (- (pow (exp x) 3) (pow 1.0 3)))
90.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series441.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(pow (exp x) 3)
218.0ms	(* (/ (exp x) (- (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
109.0ms	(/ (exp x) (- (pow (exp x) 3) (pow 1.0 3)))
66.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify1.4s

Counts

459 → 459

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	445	12521
1	1440	9045
done	5000	8107

prune2.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes177.0ms

Accuracy

97.1% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 21.6b

bsearch2.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	39
1	30	39
done	30	39

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	2640×	body	10240	exit
984.0ms	2242×	body	1280	valid
457.0ms	1648×	body	640	valid
141.0ms	855×	body	320	valid
127.0ms	2867×	body	80	valid
39.0ms	389×	body	160	valid