Details

sample539.0ms

Algorithm

intervals

Results

191.0ms	80×	body	2560	valid
129.0ms	95×	body	1280	valid
97.0ms	48×	body	10240	exit
77.0ms	45×	body	640	valid
15.0ms	304×	pre	80	true
4.0ms	9×	body	320	valid
4.0ms	22×	body	80	valid
2.0ms	5×	body	160	valid

simplify1.5s

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: 56.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
3.2b	(- (exp (* b eps)) 1)
3.4b	(- (exp (* a eps)) 1)
5.2b	(- (exp (* (+ a b) eps)) 1)

rewrite143.0ms

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:

102.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
15.0ms	(- (exp (* b eps)) 1)
11.0ms	(- (exp (* a eps)) 1)
13.0ms	(- (exp (* (+ a b) eps)) 1)

series202.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
35.0ms	(- (exp (* b eps)) 1)
36.0ms	(- (exp (* a eps)) 1)
66.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	4295
2	1271
1	377
0	154

prune670.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 44.3b

localize95.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (* 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)))
3.2b	(* eps (* (* (* eps a) (* eps a)) a))
3.2b	(- (exp (* b eps)) 1)
5.2b	(- (exp (* (+ a b) eps)) 1)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

41×	`add-cbrt-cube` `add-exp-log`
29×	`pow1`
23×	`prod-exp` `cbrt-unprod`
19×	`pow-prod-down`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
5×	`add-cube-cbrt`
4×	`frac-times` `cbrt-undiv` `div-exp` `associate-*r/` `insert-posit16` `difference-of-squares`
3×	`flip3-+` `associate-l` `flip-+`
2×	`sub-neg` `diff-log` `difference-of-sqr-1` `associate-*l/` `distribute-lft-out--` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `associate-r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

1.0s	(/ (* 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)))
215.0ms	(* eps (* (* (* eps a) (* eps a)) a))
19.0ms	(- (exp (* b eps)) 1)
27.0ms	(- (exp (* (+ a b) eps)) 1)

series1.2s

Counts

4 → 12

Calls

4 calls:

946.0ms	(/ (* 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)))
97.0ms	(* eps (* (* (* eps a) (* eps a)) a))
44.0ms	(- (exp (* b eps)) 1)
65.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.0s

Counts

109 → 109

Iterations

Iter	Nodes
2	3699
1	766
0	251

prune824.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite19.0ms

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:

19.0ms

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

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

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

simplify1.1s

Counts

23 → 23

Iterations

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

prune126.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (exp (* eps b)) 1)
4.0b	(* (/ (+ (* (* 1/2 (* eps a)) (* eps a)) (+ (* eps a) (* 1/6 (* (* eps a) (* (* eps a) (* eps a)))))) eps) (/ (- (exp (* eps b)) 1) (+ -1 (exp (* (+ b a) eps)))))
5.2b	(+ -1 (exp (* (+ b a) eps)))
16.2b	(/ (+ (* (* 1/2 (* eps a)) (* eps a)) (+ (* eps a) (* 1/6 (* (* eps a) (* (* eps a) (* eps a)))))) eps)

rewrite559.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
50×	`times-frac`
34×	`associate-r`
31×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
13×	`associate-l`
10×	`difference-of-squares`
8×	`distribute-lft-out` `add-log-exp`
6×	`pow1`
5×	`cbrt-undiv` `difference-of-sqr-1` `div-exp` `distribute-lft-out--`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr`
3×	`associate-/r` `flip3-+` `flip-+` `div-inv` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 132

Calls

4 calls:

12.0ms	(- (exp (* eps b)) 1)
250.0ms	(* (/ (+ (* (* 1/2 (* eps a)) (* eps a)) (+ (* eps a) (* 1/6 (* (* eps a) (* (* eps a) (* eps a)))))) eps) (/ (- (exp (* eps b)) 1) (+ -1 (exp (* (+ b a) eps)))))
5.0ms	(+ -1 (exp (* (+ b a) eps)))
289.0ms	(/ (+ (* (* 1/2 (* eps a)) (* eps a)) (+ (* eps a) (* 1/6 (* (* eps a) (* (* eps a) (* eps a)))))) eps)

series745.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (exp (* eps b)) 1)
480.0ms	(* (/ (+ (* (* 1/2 (* eps a)) (* eps a)) (+ (* eps a) (* 1/6 (* (* eps a) (* (* eps a) (* eps a)))))) eps) (/ (- (exp (* eps b)) 1) (+ -1 (exp (* (+ b a) eps)))))
61.0ms	(+ -1 (exp (* (+ b a) eps)))
168.0ms	(/ (+ (* (* 1/2 (* eps a)) (* eps a)) (+ (* eps a) (* 1/6 (* (* eps a) (* (* eps a) (* eps a)))))) eps)

simplify1.5s

Counts

144 → 144

Iterations

Iter	Nodes
2	2810
1	766
0	251

prune960.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

0% (3.2b remaining)

Error of 3.2b against oracle of 0.0b and baseline of 3.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	7
1	7
0	6

end0.0ms

sample19.9s

Algorithm

intervals

Results

6.5s	2494×	body	2560	valid
5.6s	3464×	body	1280	valid
5.1s	1940×	body	10240	exit
1.2s	1131×	body	640	valid
654.0ms	9942×	pre	80	true
259.0ms	342×	body	320	valid
128.0ms	426×	body	80	valid
56.0ms	145×	body	160	valid