Details

sample104.0ms

Algorithm

intervals

Results

58.0ms	78×	body	10240	exit
17.0ms	282×	body	80	valid
5.0ms	11×	body	640	valid
4.0ms	6×	body	1280	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.3b	(log (+ 1.0 (exp x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `log-div` `associate--l+` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

9.0ms	(- (log (+ 1.0 (exp x))) (* x y))
5.0ms	(+ 1.0 (exp x))
5.0ms	(log (+ 1.0 (exp x)))

series208.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(- (log (+ 1.0 (exp x))) (* x y))
14.0ms	(+ 1.0 (exp x))
118.0ms	(log (+ 1.0 (exp x)))

simplify3.2s

Counts

54 → 54

Iterations

Iter	Nodes
done	5010
4	4500
3	1537
2	529
1	211
0	92

prune258.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 3 x))
0.2b	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
0.3b	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
4.7b	(- (exp x) 1.0)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`times-frac`
15×	`log-prod`
9×	`add-exp-log`
8×	`add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`associate-/r/`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `exp-prod` `clear-num` `sub-neg` `frac-2neg` `flip3--` `exp-to-pow` `diff-log` `log-pow` `flip--` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

4 → 81

Calls

4 calls:

5.0ms	(exp (* 3 x))
80.0ms	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
26.0ms	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
8.0ms	(- (exp x) 1.0)

series317.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(exp (* 3 x))
97.0ms	(/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))
193.0ms	(log (/ (+ (* 1.0 (* 1.0 1.0)) (exp (* 3 x))) (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0))))
20.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	4126
2	1259
1	417
0	178

prune596.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* x x) 2)
0.0b	(+ (/ (* x x) 2) (+ 2.0 x))
0.0b	(- (log (+ (/ (* x x) 2) (+ 2.0 x))) (* x y))
8.8b	(log (+ (/ (* x x) 2) (+ 2.0 x)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
10×	`log-prod` `add-exp-log` `add-log-exp`
9×	`add-cbrt-cube` `distribute-lft-out`
8×	`add-sqr-sqrt` `log-div` `add-cube-cbrt`
6×	`flip3-+` `frac-add` `flip-+`
5×	`pow1` `associate--l+`
4×	`associate--l-`
3×	`associate-/r*` `sum-log` `times-frac`
2×	`cbrt-undiv` `div-exp`
1×	`+-commutative` `associate-+r+` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `cbrt-unprod` `div-inv` `flip--` `associate-/l*`

Counts

4 → 77

Calls

4 calls:

8.0ms	(/ (* x x) 2)
34.0ms	(+ (/ (* x x) 2) (+ 2.0 x))
25.0ms	(- (log (+ (/ (* x x) 2) (+ 2.0 x))) (* x y))
28.0ms	(log (+ (/ (* x x) 2) (+ 2.0 x)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (* x x) 2)
19.0ms	(+ (/ (* x x) 2) (+ 2.0 x))
93.0ms	(- (log (+ (/ (* x x) 2) (+ 2.0 x))) (* x y))
55.0ms	(log (+ (/ (* x x) 2) (+ 2.0 x)))

simplify1.7s

Counts

89 → 89

Iterations

Iter	Nodes
done	5008
2	1927
1	494
0	173

prune492.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize101.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* y x) (+ (log (+ 1.0 (exp x))) (* y x)))
0.7b	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
0.7b	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
15.6b	(/ (- (* (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (log (+ 1.0 (exp x)))) (* (* (* y x) (* y x)) (* y x))) (+ (* (* y x) (+ (log (+ 1.0 (exp x))) (* y x))) (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))))

rewrite823.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
35×	`pow1`
30×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
16×	`log-prod`
15×	`add-cbrt-cube` `add-exp-log`
12×	`times-frac` `swap-sqr` `log-pow`
11×	`associate-r`
9×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
8×	`pow3`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`difference-cubes` `distribute-lft-out` `associate-/l*` `add-log-exp`
3×	`associate-/r` `-commutative`
2×	`pow2` `flip3-+` `pow-plus` `associate-*r/` `associate-/r/` `pow-sqr` `pow-prod-up` `flip-+` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 134

Calls

4 calls:

40.0ms	(* (* y x) (+ (log (+ 1.0 (exp x))) (* y x)))
16.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
15.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
744.0ms	(/ (- (* (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (log (+ 1.0 (exp x)))) (* (* (* y x) (* y x)) (* y x))) (+ (* (* y x) (+ (log (+ 1.0 (exp x))) (* y x))) (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (* y x) (+ (log (+ 1.0 (exp x))) (* y x)))
130.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
115.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
346.0ms	(/ (- (* (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (log (+ 1.0 (exp x)))) (* (* (* y x) (* y x)) (* y x))) (+ (* (* y x) (+ (log (+ 1.0 (exp x))) (* y x))) (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))))

simplify2.5s

Counts

146 → 146

Iterations

Iter	Nodes
done	5004
2	2403
1	589
0	203

prune799.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes97.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.2s	2504×	body	10240	exit
640.0ms	8461×	body	80	valid
141.0ms	253×	body	640	valid
92.0ms	124×	body	1280	valid
48.0ms	189×	body	320	valid
14.0ms	100×	body	160	valid