Details

sample516.0ms

Algorithm

intervals

Results

190.0ms	81×	body	2560	valid
131.0ms	106×	body	1280	valid
106.0ms	38×	body	10240	exit
31.0ms	38×	body	640	valid
15.0ms	294×	pre	80	true
9.0ms	14×	body	320	valid
2.0ms	13×	body	80	valid
2.0ms	4×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4181
4	694
3	215
2	98
1	43
0	17

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.6b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
1.4b	(- (exp (* a eps)) 1)
3.3b	(- (exp (* b eps)) 1)
3.5b	(- (exp (* (+ a b) eps)) 1)

rewrite701.0ms

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:

389.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
40.0ms	(- (exp (* a eps)) 1)
50.0ms	(- (exp (* b eps)) 1)
219.0ms	(- (exp (* (+ a b) eps)) 1)

series247.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
60.0ms	(- (exp (* a eps)) 1)
54.0ms	(- (exp (* b eps)) 1)
49.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	4593
2	1367
1	395
0	154

prune776.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 45.5b

localize78.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
2.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
2.5b	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
3.5b	(- (exp (* (+ a b) eps)) 1)

rewrite3.5m

Algorithm

rewrite-expression-head

Rules

1028×	`associate-r`
975×	`associate-l`
900×	`*-un-lft-identity`
588×	`add-sqr-sqrt`
560×	`times-frac`
399×	`distribute-lft-out`
203×	`add-cube-cbrt`
110×	`difference-of-squares`
95×	`distribute-rgt-out`
92×	`*-commutative`
55×	`difference-of-sqr-1` `distribute-lft-out--`
54×	`unswap-sqr`
35×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
12×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
9×	`+-commutative`
8×	`frac-times` `flip3--` `associate-/r/` `flip--` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`pow1` `associate-*r/`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `insert-posit16`
2×	`associate-/l/`
1×	`clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `div-inv`

Counts

4 → 754

Calls

4 calls:

23.4s	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
1.6m	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
1.6m	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
615.0ms	(- (exp (* (+ a b) eps)) 1)

series1.7s

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
1.4s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
205.0ms	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
55.0ms	(- (exp (* (+ a b) eps)) 1)

simplify1.7s

Counts

766 → 766

Iterations

Iter	Nodes
done	5004
1	2758
0	774

prune2.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune14.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (exp (* a eps)) 1)
2.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (* (* b eps) (+ (* (* (* b eps) (* b eps)) 1/6) (+ 1 (* 1/2 (* b eps)))))))
2.5b	(* (- (exp (* a eps)) 1) (* (* b eps) (+ (* (* (* b eps) (* b eps)) 1/6) (+ 1 (* 1/2 (* b eps))))))
3.5b	(- (exp (* (+ a b) eps)) 1)

rewrite17.7s

Algorithm

rewrite-expression-head

Rules

1286×	`associate-r`
1065×	`*-un-lft-identity`
947×	`add-sqr-sqrt`
942×	`associate-l`
784×	`times-frac`
360×	`distribute-lft-out`
279×	`add-cube-cbrt`
230×	`unswap-sqr`
140×	`difference-of-squares`
104×	`*-commutative`
70×	`difference-of-sqr-1` `distribute-lft-out--`
49×	`associate-/r*`
45×	`add-cbrt-cube` `add-exp-log`
22×	`prod-exp` `cbrt-unprod`
18×	`associate-*r/`
16×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
13×	`pow1`
9×	`flip3--` `flip--`
8×	`frac-times` `cbrt-undiv` `+-commutative` `associate-+r+` `div-exp` `associate-/r/` `add-log-exp`
6×	`flip3-+` `pow-prod-down` `flip-+`
4×	`associate-*l/` `insert-posit16`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`clear-num` `frac-2neg` `div-inv`

Counts

4 → 1006

Calls

4 calls:

38.0ms	(- (exp (* a eps)) 1)
10.9s	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (* (* b eps) (+ (* (* (* b eps) (* b eps)) 1/6) (+ 1 (* 1/2 (* b eps)))))))
6.5s	(* (- (exp (* a eps)) 1) (* (* b eps) (+ (* (* (* b eps) (* b eps)) 1/6) (+ 1 (* 1/2 (* b eps))))))
151.0ms	(- (exp (* (+ a b) eps)) 1)

series1.0s

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (exp (* a eps)) 1)
731.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (* (* b eps) (+ (* (* (* b eps) (* b eps)) 1/6) (+ 1 (* 1/2 (* b eps)))))))
195.0ms	(* (- (exp (* a eps)) 1) (* (* b eps) (+ (* (* (* b eps) (* b eps)) 1/6) (+ 1 (* 1/2 (* b eps))))))
46.0ms	(- (exp (* (+ a b) eps)) 1)

simplify2.2s

Counts

1018 → 1018

Iterations

Iter	Nodes
done	5000
1	4619
0	1132

prune3.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes109.0ms

Accuracy

0% (2.9b remaining)

Error of 3.2b against oracle of 0.3b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample12.5s

Algorithm

intervals

Results

4.6s	2619×	body	2560	valid
3.6s	3428×	body	1280	valid
2.9s	1908×	body	10240	exit
664.0ms	1041×	body	640	valid
296.0ms	9909×	pre	80	true
139.0ms	339×	body	320	valid
68.0ms	427×	body	80	valid
34.0ms	147×	body	160	valid