Details

sample474.0ms

Algorithm

intervals

Results

184.0ms	85×	body	2560	valid
127.0ms	114×	body	1280	valid
102.0ms	57×	body	10240	exit
24.0ms	33×	body	640	valid
12.0ms	313×	pre	80	true
2.0ms	15×	body	80	valid
2.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	853
3	236
2	101
1	43
0	17

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.5b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
2.3b	(- (exp (* a eps)) 1)
3.9b	(- (exp (* b eps)) 1)
4.7b	(- (exp (* (+ a b) eps)) 1)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
10×	`add-log-exp` `difference-of-squares`
9×	`flip3--` `flip--`
7×	`associate-r` `associate-l`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`sub-neg` `difference-of-sqr-1` `distribute-lft-out--`
4×	`frac-times` `insert-posit16`
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 → 90

Calls

4 calls:

63.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
11.0ms	(- (exp (* a eps)) 1)
12.0ms	(- (exp (* b eps)) 1)
16.0ms	(- (exp (* (+ a b) eps)) 1)

series166.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
34.0ms	(- (exp (* a eps)) 1)
32.0ms	(- (exp (* b eps)) 1)
50.0ms	(- (exp (* (+ a b) eps)) 1)

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1481
1	395
0	154

prune677.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 45.9b

localize89.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (+ (* eps b) (* (* 1/2 (* eps b)) (* eps b))))))
3.4b	(* b (* (* 1/6 eps) (* (* eps b) (* eps b))))
3.9b	(* (- (exp (* a eps)) 1) (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (+ (* eps b) (* (* 1/2 (* eps b)) (* eps b)))))
4.7b	(- (exp (* (+ a b) eps)) 1)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

71×	`add-cbrt-cube` `add-exp-log`
59×	`pow1`
47×	`prod-exp` `cbrt-unprod`
43×	`pow-prod-down`
17×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`associate-l`
8×	`frac-times` `flip3--` `associate-/r/` `flip--`
7×	`add-cube-cbrt`
6×	`flip3-+` `associate-*r/` `flip-+` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-r` `associate-*l/` `insert-posit16` `difference-of-squares`
2×	`difference-of-sqr-1` `*-commutative` `distribute-lft-out--` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `distribute-lft-in` `times-frac` `diff-log` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 128

Calls

4 calls:

303.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (+ (* eps b) (* (* 1/2 (* eps b)) (* eps b))))))
165.0ms	(* b (* (* 1/6 eps) (* (* eps b) (* eps b))))
783.0ms	(* (- (exp (* a eps)) 1) (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (+ (* eps b) (* (* 1/2 (* eps b)) (* eps b)))))
16.0ms	(- (exp (* (+ a b) eps)) 1)

series2.2s

Counts

4 → 12

Calls

4 calls:

1.8s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (+ (* eps b) (* (* 1/2 (* eps b)) (* eps b))))))
99.0ms	(* b (* (* 1/6 eps) (* (* eps b) (* eps b))))
242.0ms	(* (- (exp (* a eps)) 1) (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (+ (* eps b) (* (* 1/2 (* eps b)) (* eps b)))))
58.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.6s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
1	1045
0	307

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

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-+` `insert-posit16`

Counts

1 → 20

Calls

1 calls:

21.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify2.8s

Counts

23 → 23

Iterations

Iter	Nodes
done	5035
5	3477
4	1389
3	623
2	282
1	105
0	41

prune79.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

16.0b

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

rewrite21.0ms

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-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 26

Calls

1 calls:

20.0ms

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

series47.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

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

simplify3.1s

Counts

29 → 29

Iterations

Iter	Nodes
done	5000
3	1674
2	492
1	146
0	56

prune101.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes135.0ms

Accuracy

0% (2.8b remaining)

Error of 2.9b against oracle of 0.1b and baseline of 2.9b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample19.9s

Algorithm

intervals

Results

6.3s	2592×	body	2560	valid
6.0s	1994×	body	10240	exit
5.0s	3421×	body	1280	valid
1.1s	1100×	body	640	valid
666.0ms	9995×	pre	80	true
225.0ms	383×	body	320	valid
97.0ms	389×	body	80	valid
68.0ms	116×	body	160	valid