Details

sample57.0ms

Algorithm

intervals

Results

39.0ms	90×	body	10240	exit
7.0ms	256×	body	80	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	222
1	7	222
done	7	222

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
1.0b	(/ (exp a) (+ (exp a) (exp b)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

8.0ms	(+ (exp a) (exp b))
27.0ms	(/ (exp a) (+ (exp a) (exp b)))

series64.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ (exp a) (exp b))
41.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify2.0s

Counts

58 → 58

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	82	18403
1	184	17355
2	626	17225
3	3653	17123
done	5001	17107

prune214.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- a (log (+ (exp a) (exp b)))))
0.0b	(+ (exp a) (exp b))
1.4b	(- a (log (+ (exp a) (exp b))))
3.7b	(log (+ (exp a) (exp b)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
24×	`prod-diff`
23×	`add-cube-cbrt`
16×	`exp-sum`
13×	`pow1`
9×	`log-pow` `add-log-exp`
8×	`log-prod`
6×	`log-div` `exp-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `associate--r+` `distribute-lft-out--` `associate--r-`
3×	`fma-def` `fma-neg` `distribute-lft-out`
2×	`sub-neg` `diff-log` `difference-of-squares` `rem-exp-log`
1×	`+-commutative` `sum-log` `flip3--` `exp-diff` `rem-log-exp` `flip--`

Counts

4 → 106

Calls

4 calls:

22.0ms	(exp (- a (log (+ (exp a) (exp b)))))
8.0ms	(+ (exp a) (exp b))
15.0ms	(- a (log (+ (exp a) (exp b))))
13.0ms	(log (+ (exp a) (exp b)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(exp (- a (log (+ (exp a) (exp b)))))
30.0ms	(+ (exp a) (exp b))
56.0ms	(- a (log (+ (exp a) (exp b))))
37.0ms	(log (+ (exp a) (exp b)))

simplify1.4s

Counts

118 → 118

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	149	56534
1	328	49708
2	1235	43474
done	5002	35398

prune520.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* 1/2 (- a b)) (log 2))
0.0b	(exp (- (* 1/2 (- a b)) (log 2)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 87

Calls

2 calls:

15.0ms	(- (* 1/2 (- a b)) (log 2))
37.0ms	(exp (- (* 1/2 (- a b)) (log 2)))

series105.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (* 1/2 (- a b)) (log 2))
51.0ms	(exp (- (* 1/2 (- a b)) (log 2)))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	182	38677
1	419	31592
2	1646	25055
done	5000	23588

prune382.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize104.0ms

Local error

Found 4 expressions with local error:

1.4b	(- a (- (log (fma (exp b) (* (exp b) (exp b)) (exp (fma 2 a a)))) (log (fma (exp a) (exp a) (* (exp b) (- (exp b) (exp a)))))))
3.2b	(- (exp b) (exp a))
3.7b	(log (fma (exp b) (* (exp b) (exp b)) (exp (fma 2 a a))))
6.9b	(log (fma (exp a) (exp a) (* (exp b) (- (exp b) (exp a)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
49×	`prod-diff`
44×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
30×	`pow1`
26×	`log-pow`
22×	`distribute-lft-out--`
21×	`associate--r+`
9×	`log-prod` `add-log-exp`
6×	`fma-neg` `add-exp-log`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `add-cbrt-cube` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+`
2×	`flip3--` `rem-log-exp` `flip--`
1×	`associate--r-`

Counts

4 → 126

Calls

4 calls:

23.0ms	(- a (- (log (fma (exp b) (* (exp b) (exp b)) (exp (fma 2 a a)))) (log (fma (exp a) (exp a) (* (exp b) (- (exp b) (exp a)))))))
17.0ms	(- (exp b) (exp a))
2.0ms	(log (fma (exp b) (* (exp b) (exp b)) (exp (fma 2 a a))))
2.0ms	(log (fma (exp a) (exp a) (* (exp b) (- (exp b) (exp a)))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(- a (- (log (fma (exp b) (* (exp b) (exp b)) (exp (fma 2 a a)))) (log (fma (exp a) (exp a) (* (exp b) (- (exp b) (exp a)))))))
28.0ms	(- (exp b) (exp a))
69.0ms	(log (fma (exp b) (* (exp b) (exp b)) (exp (fma 2 a a))))
114.0ms	(log (fma (exp a) (exp a) (* (exp b) (- (exp b) (exp a)))))

simplify2.8s

Counts

138 → 138

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	217	109637
1	488	102598
2	1991	93560
done	5002	77720

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

regimes252.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	222
1	7	222
done	7	222

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.8s	3525×	body	10240	exit
377.0ms	8000×	body	80	valid