Details

sample405.0ms

Algorithm

intervals

Results

178.0ms	88×	body	2560	valid
84.0ms	101×	body	1280	valid
83.0ms	59×	body	10240	exit
22.0ms	46×	body	640	valid
8.0ms	315×	pre	80	true
5.0ms	14×	body	320	valid
1.0ms	5×	body	80	valid
0.0ms	2×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (229.0ms)

Iter	Nodes	Cost
0	17	614
1	40	614
2	101	614
3	245	614
4	699	584
5	3569	584
done	5001	584

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 62.7b

localize67.0ms

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)

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

87.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
19.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* a eps)) 1.0)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)

series226.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
40.0ms	(- (exp (* b eps)) 1.0)
49.0ms	(- (exp (* a eps)) 1.0)
69.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.4s

Counts

88 → 88

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	143	35034
1	356	30429
2	1625	30429
done	5001	30310

prune966.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 53.8b

localize93.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* a eps) (* 1/6 (* (* eps (* eps eps)) (* a (* a a))))) (* (* (* eps eps) (* a a)) 1/2)) (- (exp (* b eps)) 1.0)))
5.6b	(- (exp (* (+ a b) eps)) 1.0)
12.5b	(* (* eps eps) (* a a))
15.2b	(* (* eps (* eps eps)) (* a (* a a)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

96×	`pow1`
64×	`add-cbrt-cube` `add-exp-log`
48×	`pow-prod-down`
39×	`prod-exp` `cbrt-unprod`
20×	`pow-prod-up`
8×	`pow-plus` `associate-/r/`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow2` `frac-times` `cbrt-undiv` `div-exp` `associate-*r/` `pow-sqr` `add-cube-cbrt`
3×	`flip3-+` `flip-+`
2×	`cube-unmult` `associate-r` `associate-l` `associate-l/` `-commutative` `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` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

93.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* a eps) (* 1/6 (* (* eps (* eps eps)) (* a (* a a))))) (* (* (* eps eps) (* a a)) 1/2)) (- (exp (* b eps)) 1.0)))
11.0ms	(- (exp (* (+ a b) eps)) 1.0)
25.0ms	(* (* eps eps) (* a a))
100.0ms	(* (* eps (* eps eps)) (* a (* a a)))

series1.3s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* a eps) (* 1/6 (* (* eps (* eps eps)) (* a (* a a))))) (* (* (* eps eps) (* a a)) 1/2)) (- (exp (* b eps)) 1.0)))
56.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (* eps eps) (* a a))
93.0ms	(* (* eps (* eps eps)) (* a (* a a)))

simplify2.1s

Counts

130 → 130

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	248	61733
1	866	53664
done	5000	52522

prune974.0ms

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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+`

Counts

1 → 19

Calls

1 calls:

39.0ms

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

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

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

simplify1.5s

Counts

22 → 22

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	40	4292
1	102	3720
2	381	3720
3	1500	3720
done	5000	3720

prune134.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

13.1b

(/ (+ a b) (* a b))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-cbrt-cube` `add-exp-log`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `distribute-lft-out` `associate-/l/`
1×	`pow1` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 25

Calls

1 calls:

33.0ms

(/ (+ a b) (* a b))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(/ (+ a b) (* a b))

simplify2.7s

Counts

28 → 28

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	55	5240
1	145	5030
2	512	4790
3	2182	4790
done	5000	4790

prune120.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes197.0ms

Accuracy

0% (3.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	123
1	9	123
done	9	123

end0.0ms

sample15.4s

Algorithm

intervals

Results

5.6s	2650×	body	2560	valid
3.9s	2013×	body	10240	exit
3.4s	3337×	body	1280	valid
1.4s	1088×	body	640	valid
310.0ms	10016×	pre	80	true
125.0ms	358×	body	320	valid
87.0ms	463×	body	80	valid
26.0ms	107×	body	160	valid