Details

sample384.0ms

Algorithm

intervals

Results

121.0ms	88×	body	2560	valid
117.0ms	59×	body	10240	exit
78.0ms	101×	body	1280	valid
20.0ms	46×	body	640	valid
7.0ms	315×	pre	80	true
4.0ms	14×	body	320	valid
0.0ms	5×	body	80	valid
0.0ms	2×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4020
4	765
3	258
2	101
1	40
0	17

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 62.7b

localize83.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
4.2b	(- (exp (* a eps)) 1.0)
5.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-l/` `associate-r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

59.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
19.0ms	(- (exp (* b eps)) 1.0)
11.0ms	(- (exp (* a eps)) 1.0)
12.0ms	(- (exp (* (+ a b) eps)) 1.0)

series280.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
43.0ms	(- (exp (* b eps)) 1.0)
58.0ms	(- (exp (* a eps)) 1.0)
77.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.7s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2587
1	540
0	221

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 53.8b

localize95.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))) (- (exp (* b eps)) 1.0)))
5.6b	(- (exp (* (+ a b) eps)) 1.0)
10.2b	(fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a)))
12.9b	(fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`associate-/r/` `fma-udef` `associate-/l/`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `diff-log` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

68.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))) (- (exp (* b eps)) 1.0)))
23.0ms	(- (exp (* (+ a b) eps)) 1.0)
1.0ms	(fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a)))
1.0ms	(fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))) (- (exp (* b eps)) 1.0)))
65.0ms	(- (exp (* (+ a b) eps)) 1.0)
189.0ms	(fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a)))
196.0ms	(fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))

simplify3.5s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	3138
1	580
0	207

prune654.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 a) (/ 1 b))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

32.0ms

(+ (/ 1 a) (/ 1 b))

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

(+ (/ 1 a) (/ 1 b))

simplify2.5s

Counts

37 → 37

Iterations

Iter	Nodes
done	5000
3	2236
2	439
1	110
0	42

prune177.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
0.6b	(cbrt (/ 1 a))
0.6b	(cbrt (/ 1 a))
0.6b	(cbrt (/ 1 a))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 161

Calls

4 calls:

21.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
2.0ms	(cbrt (/ 1 a))
2.0ms	(cbrt (/ 1 a))
2.0ms	(cbrt (/ 1 a))

series998.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
256.0ms	(cbrt (/ 1 a))
211.0ms	(cbrt (/ 1 a))
278.0ms	(cbrt (/ 1 a))

simplify1.7s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	1088
1	255
0	143

prune875.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes270.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample15.0s

Algorithm

intervals

Results

5.1s	2650×	body	2560	valid
3.7s	3337×	body	1280	valid
3.7s	2013×	body	10240	exit
772.0ms	10016×	pre	80	true
626.0ms	1088×	body	640	valid
570.0ms	358×	body	320	valid
46.0ms	463×	body	80	valid
23.0ms	107×	body	160	valid