Details

sample616.0ms

Algorithm

intervals

Results

197.0ms	79×	body	2560	valid
193.0ms	74×	body	10240	exit
146.0ms	115×	body	1280	valid
29.0ms	37×	body	640	valid
16.0ms	330×	pre	80	true
6.0ms	10×	body	320	valid
2.0ms	10×	body	80	valid
2.0ms	5×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
5	4055
4	686
3	213
2	96
1	41
0	17

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 59.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
2.5b	(- (exp (* b eps)) 1)
4.1b	(- (exp (* a eps)) 1)
5.4b	(- (exp (* (+ a b) eps)) 1)

rewrite140.0ms

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:

83.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
21.0ms	(- (exp (* b eps)) 1)
20.0ms	(- (exp (* a eps)) 1)
13.0ms	(- (exp (* (+ a b) eps)) 1)

series211.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
32.0ms	(- (exp (* b eps)) 1)
38.0ms	(- (exp (* a eps)) 1)
71.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.5s

Counts

102 → 102

Iterations

Iter	Nodes
3	4295
2	1271
1	377
0	154

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 47.3b

localize85.0ms

Local error

Found 4 expressions with local error:

2.9b	(* eps (* (* (* eps a) (* eps a)) a))
3.2b	(* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1))
3.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
5.4b	(- (exp (* (+ a b) eps)) 1)

rewrite4.7s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

223.0ms	(* eps (* (* (* eps a) (* eps a)) a))
3.5s	(* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1))
991.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
20.0ms	(- (exp (* (+ a b) eps)) 1)

series1.2s

Counts

4 → 12

Calls

4 calls:

61.0ms	(* eps (* (* (* eps a) (* eps a)) a))
148.0ms	(* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1))
978.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
49.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.6s

Counts

127 → 127

Iterations

Iter	Nodes
2	4387
1	883
0	274

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite22.0ms

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))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify1.0s

Counts

23 → 23

Iterations

Iter	Nodes
4	2330
3	898
2	363
1	101
0	41

prune147.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

14.6b

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

rewrite22.0ms

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:

22.0ms

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

series65.0ms

Counts

1 → 3

Calls

1 calls:

65.0ms

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

simplify4.3s

Counts

29 → 29

Iterations

Iter	Nodes
4	6147
3	1932
2	534
1	147
0	57

prune209.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes184.0ms

Accuracy

0% (3.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	7
1	7
0	6

end0.0ms

sample20.1s

Algorithm

intervals

Results

7.8s	2655×	body	2560	valid
4.8s	3372×	body	1280	valid
4.5s	1955×	body	10240	exit
1.4s	1043×	body	640	valid
776.0ms	9958×	pre	80	true
205.0ms	344×	body	320	valid
85.0ms	466×	body	80	valid
82.0ms	123×	body	160	valid