Details

sample115.0ms

Algorithm

intervals

Results

83.0ms	115×	body	10240	exit
11.0ms	256×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
done	7	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

22.0ms	(+ (exp a) (exp b))
42.0ms	(/ (exp a) (+ (exp a) (exp b)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(+ (exp a) (exp b))
82.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify2.1s

Counts

58 → 58

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	82	646
1	184	616
2	636	576
3	3574	575
done	5001	574

prune190.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- a (log (+ (exp a) (exp b)))))
0.0b	(+ (exp a) (exp b))
0.6b	(- a (log (+ (exp a) (exp b))))
3.8b	(log (+ (exp a) (exp b)))

rewrite128.0ms

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` `rem-exp-log` `difference-of-squares`
1×	`+-commutative` `flip3--` `exp-diff` `rem-log-exp` `sum-log` `flip--`

Counts

4 → 106

Calls

4 calls:

43.0ms	(exp (- a (log (+ (exp a) (exp b)))))
22.0ms	(+ (exp a) (exp b))
39.0ms	(- a (log (+ (exp a) (exp b))))
18.0ms	(log (+ (exp a) (exp b)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(exp (- a (log (+ (exp a) (exp b)))))
37.0ms	(+ (exp a) (exp b))
64.0ms	(- a (log (+ (exp a) (exp b))))
53.0ms	(log (+ (exp a) (exp b)))

simplify1.3s

Counts

118 → 118

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	149	2147
1	327	1622
2	1236	1280
done	5000	1065

prune365.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp a) (exp b)))
0.0b	(sqrt (+ (exp a) (exp b)))
0.3b	(* (sqrt (+ (exp a) (exp b))) (sqrt (+ (exp a) (exp b))))
1.0b	(/ (exp a) (* (sqrt (+ (exp a) (exp b))) (sqrt (+ (exp a) (exp b)))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
28×	`sqrt-div`
21×	`pow1`
16×	`add-cube-cbrt`
14×	`flip3-+` `flip-+`
11×	`swap-sqr` `add-cbrt-cube`
10×	`sqrt-pow1` `pow1/2`
9×	`add-exp-log`
8×	`frac-times` `associate-/r/` `distribute-lft-out`
7×	`associate-r` `associate-l`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`times-frac` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod` `hypot-def`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv`

Counts

4 → 133

Calls

4 calls:

32.0ms	(sqrt (+ (exp a) (exp b)))
24.0ms	(sqrt (+ (exp a) (exp b)))
127.0ms	(* (sqrt (+ (exp a) (exp b))) (sqrt (+ (exp a) (exp b))))
66.0ms	(/ (exp a) (* (sqrt (+ (exp a) (exp b))) (sqrt (+ (exp a) (exp b)))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (+ (exp a) (exp b)))
62.0ms	(sqrt (+ (exp a) (exp b)))
30.0ms	(* (sqrt (+ (exp a) (exp b))) (sqrt (+ (exp a) (exp b))))
46.0ms	(/ (exp a) (* (sqrt (+ (exp a) (exp b))) (sqrt (+ (exp a) (exp b)))))

simplify2.2s

Counts

145 → 145

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	140	2338
1	314	1539
2	1267	1405
done	5000	1385

prune497.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma b 1/2 (log 2))
15.0ms	(- (* 1/2 a) (fma b 1/2 (log 2)))
37.0ms	(exp (- (* 1/2 a) (fma b 1/2 (log 2))))

series403.0ms

Counts

3 → 9

Calls

3 calls:

266.0ms	(fma b 1/2 (log 2))
55.0ms	(- (* 1/2 a) (fma b 1/2 (log 2)))
82.0ms	(exp (- (* 1/2 a) (fma b 1/2 (log 2))))

simplify702.0ms

Counts

58 → 58

Iterations

Useful iterations: done (699.0ms)

Iter	Nodes	Cost
0	86	866
1	185	707
2	825	604
done	5000	542

prune227.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes138.0ms

Accuracy

0% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
done	7	8

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.2s	3577×	body	10240	exit
668.0ms	8000×	body	80	valid