Details

sample147.0ms

Algorithm

intervals

Results

86.0ms	99×	body	10240	exit
22.0ms	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

simplify27.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

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)))

rewrite86.0ms

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:

58.0ms	(- (log (+ 1.0 (exp x))) (* x y))
13.0ms	(+ 1.0 (exp x))
11.0ms	(log (+ 1.0 (exp x)))

series749.0ms

Counts

3 → 9

Calls

3 calls:

157.0ms	(- (log (+ 1.0 (exp x))) (* x y))
472.0ms	(+ 1.0 (exp x))
120.0ms	(log (+ 1.0 (exp x)))

simplify3.6s

Counts

71 → 71

Iterations

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

prune522.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
1.2b	(log (sqrt (+ 1.0 (exp x))))
1.2b	(log (sqrt (+ 1.0 (exp x))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

15.0ms	(+ 1.0 (exp x))
37.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
13.0ms	(log (sqrt (+ 1.0 (exp x))))
15.0ms	(log (sqrt (+ 1.0 (exp x))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (exp x))
273.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
301.0ms	(log (sqrt (+ 1.0 (exp x))))
229.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify3.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
3	2145
2	661
1	266
0	124

prune987.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize69.0ms

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)))

rewrite162.0ms

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)))
15.0ms	(log (+ 1.0 (exp x)))
23.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
107.0ms	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

series726.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(log (+ 1.0 (exp x)))
119.0ms	(log (+ 1.0 (exp x)))
190.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
291.0ms	(/ (- (* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x)))) (* (* x y) (* x y))) (+ (log (+ 1.0 (exp x))) (* x y)))

simplify3.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5002
2	1533
1	474
0	174

prune976.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
9.3b	(log (fma (fma 1/2 x 1) x 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
5×	`pow1`
4×	`fma-neg` `prod-diff`
3×	`add-exp-log` `associate--l+` `log-pow` `add-log-exp`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 39

Calls

2 calls:

18.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
3.0ms	(log (fma (fma 1/2 x 1) x 2.0))

series333.0ms

Counts

2 → 6

Calls

2 calls:

199.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
134.0ms	(log (fma (fma 1/2 x 1) x 2.0))

simplify3.1s

Counts

45 → 45

Iterations

Iter	Nodes
done	5005
3	1951
2	607
1	222
0	93

prune386.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes185.0ms

Accuracy

0% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	2450×	body	10240	exit
1.4s	8429×	body	80	valid
129.0ms	244×	body	640	valid
128.0ms	136×	body	1280	valid
56.0ms	167×	body	320	valid
20.0ms	105×	body	160	valid