Details

sample166.0ms

Algorithm

intervals

Results

105.0ms	99×	body	10240	exit
24.0ms	272×	body	80	valid
7.0ms	13×	body	640	valid
2.0ms	6×	body	320	valid
2.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
3	23
2	19
1	12
0	8

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.5b	(log (+ 1.0 (exp x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `fma-neg` `prod-diff` `associate--l+`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `flip--`

Counts

3 → 62

Calls

3 calls:

28.0ms	(- (log (+ 1.0 (exp x))) (* x y))
10.0ms	(+ 1.0 (exp x))
10.0ms	(log (+ 1.0 (exp x)))

series301.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(- (log (+ 1.0 (exp x))) (* x y))
16.0ms	(+ 1.0 (exp x))
182.0ms	(log (+ 1.0 (exp x)))

simplify3.8s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	1972
2	627
1	241
0	105

prune581.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.2b	(log (sqrt (+ 1.0 (exp x))))
1.2b	(log (sqrt (+ 1.0 (exp x))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`add-exp-log` `fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log`

Counts

4 → 78

Calls

4 calls:

18.0ms	(+ 1.0 (exp x))
12.0ms	(+ 1.0 (exp x))
14.0ms	(log (sqrt (+ 1.0 (exp x))))
32.0ms	(log (sqrt (+ 1.0 (exp x))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ 1.0 (exp x))
15.0ms	(+ 1.0 (exp x))
204.0ms	(log (sqrt (+ 1.0 (exp x))))
188.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify3.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
4	2296
3	911
2	380
1	168
0	84

prune950.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (+ 1.0 (exp x)))
0.5b	(log (+ 1.0 (exp x)))
0.6b	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
12.4b	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
19×	`pow1`
16×	`log-prod`
12×	`times-frac`
10×	`add-exp-log`
8×	`log-pow` `add-cbrt-cube`
6×	`swap-sqr`
4×	`distribute-rgt-in` `expm1-log1p-u` `log-div` `distribute-lft-in` `associate-r` `associate-l` `log1p-expm1-u` `distribute-lft-out` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`rem-log-exp` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `flip3--` `frac-2neg` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

11.0ms	(log (+ 1.0 (exp x)))
11.0ms	(log (+ 1.0 (exp x)))
42.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
96.0ms	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

series704.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(log (+ 1.0 (exp x)))
129.0ms	(log (+ 1.0 (exp x)))
170.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
281.0ms	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

simplify2.9s

Counts

124 → 124

Iterations

Iter	Nodes
done	5002
2	1533
1	474
0	174

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (log (+ 1.0 (exp x))) (* x y)) (- (log (+ 1.0 (exp x))) (* x y)))
0.5b	(log (+ 1.0 (exp x)))
0.5b	(log (+ 1.0 (exp x)))
0.5b	(log (+ 1.0 (exp x)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`log-prod`
9×	`add-exp-log` `times-frac`
8×	`log-div`
7×	`pow1`
6×	`add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp` `associate-/r` `log-pow` `distribute-lft-out` `associate-/l`
2×	`associate-+l-` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 86

Calls

4 calls:

73.0ms	(/ (+ (log (+ 1.0 (exp x))) (* x y)) (- (log (+ 1.0 (exp x))) (* x y)))
12.0ms	(log (+ 1.0 (exp x)))
12.0ms	(log (+ 1.0 (exp x)))
12.0ms	(log (+ 1.0 (exp x)))

series811.0ms

Counts

4 → 12

Calls

4 calls:

416.0ms	(/ (+ (log (+ 1.0 (exp x))) (* x y)) (- (log (+ 1.0 (exp x))) (* x y)))
130.0ms	(log (+ 1.0 (exp x)))
139.0ms	(log (+ 1.0 (exp x)))
125.0ms	(log (+ 1.0 (exp x)))

simplify4.5s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
3	4275
2	1099
1	348
0	141

prune920.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes193.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.9s	2450×	body	10240	exit
796.0ms	8429×	body	80	valid
611.0ms	167×	body	320	valid
140.0ms	136×	body	1280	valid
128.0ms	244×	body	640	valid
20.0ms	105×	body	160	valid