Details

sample60.0ms

Algorithm

intervals

Results

44.0ms	111×	body	10240	exit
6.0ms	256×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.7b	(/ (exp a) (+ (exp a) (exp b)))

rewrite15.0ms

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:

4.0ms	(+ (exp a) (exp b))
9.0ms	(/ (exp a) (+ (exp a) (exp b)))

series55.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ (exp a) (exp b))
32.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify3.0s

Counts

58 → 58

Iterations

Useful iterations: 4 (909.0ms)

Iter	Nodes	Cost
0	82	646
1	183	616
2	501	576
3	1222	575
4	3805	574
done	5000	574

prune131.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- a (log (+ (exp a) (exp b))))
0.0b	(+ (exp a) (exp b))
2.9b	(log (+ (exp a) (exp b)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

14.0ms	(- a (log (+ (exp a) (exp b))))
9.0ms	(+ (exp a) (exp b))
7.0ms	(log (+ (exp a) (exp b)))

series93.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- a (log (+ (exp a) (exp b))))
17.0ms	(+ (exp a) (exp b))
38.0ms	(log (+ (exp a) (exp b)))

simplify1.1s

Counts

81 → 81

Iterations

Useful iterations: 3 (265.0ms)

Iter	Nodes	Cost
0	110	1259
1	245	985
2	601	818
3	2102	797
done	5000	797

prune203.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (exp a) (exp b))
0.7b	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
0.7b	(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
2.6b	(- (* (exp b) (exp b)) (* (exp a) (exp b)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
55×	`times-frac`
41×	`add-sqr-sqrt`
36×	`associate-l`
35×	`distribute-lft-out`
34×	`add-cube-cbrt`
28×	`unpow-prod-down` `cube-prod`
13×	`add-cbrt-cube`
9×	`add-exp-log` `associate-/r*`
8×	`pow1`
7×	`sum-cubes`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `exp-prod` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `distribute-lft-in` `fma-neg` `diff-log` `prod-diff` `associate-*l/` `clear-num` `pow-prod-up` `flip--`

Counts

4 → 153

Calls

4 calls:

7.0ms	(* (exp a) (exp b))
31.0ms	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
157.0ms	(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
7.0ms	(- (* (exp b) (exp b)) (* (exp a) (exp b)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (exp a) (exp b))
63.0ms	(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
144.0ms	(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
42.0ms	(- (* (exp b) (exp b)) (* (exp a) (exp b)))

simplify1.4s

Counts

165 → 165

Iterations

Useful iterations: 2 (250.0ms)

Iter	Nodes	Cost
0	221	3863
1	691	3274
2	3642	2975
done	5000	2975

prune478.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`exp-sum`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
5×	`exp-prod`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`fma-udef` `rem-exp-log`
1×	`sub-neg` `exp-diff` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 48

Calls

3 calls:

0.0ms	(fma a 1/2 (fma b 1/2 (log 2)))
0.0ms	(fma b 1/2 (log 2))
8.0ms	(exp (- a (fma a 1/2 (fma b 1/2 (log 2)))))

series245.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(fma a 1/2 (fma b 1/2 (log 2)))
161.0ms	(fma b 1/2 (log 2))
53.0ms	(exp (- a (fma a 1/2 (fma b 1/2 (log 2)))))

simplify1.1s

Counts

57 → 57

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	97	1116
1	163	832
2	463	653
3	2264	527
done	5001	502

prune132.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes74.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	9	9
done	9	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	3481×	body	10240	exit
203.0ms	8000×	body	80	valid