Details

sample358.0ms

Algorithm

intervals

Results

118.0ms	81×	body	2560	valid
94.0ms	106×	body	1280	valid
87.0ms	38×	body	10240	exit
21.0ms	38×	body	640	valid
9.0ms	294×	pre	80	true
5.0ms	14×	body	320	valid
2.0ms	13×	body	80	valid
1.0ms	4×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.6b

localize40.0ms

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)

rewrite137.0ms

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:

82.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
12.0ms	(- (exp (* a eps)) 1)
23.0ms	(- (exp (* b eps)) 1)
19.0ms	(- (exp (* (+ a b) eps)) 1)

series214.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
40.0ms	(- (exp (* a eps)) 1)
44.0ms	(- (exp (* b eps)) 1)
60.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.1s

Counts

102 → 102

Iterations

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

prune605.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 45.5b

localize76.0ms

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)

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

332.0ms	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
603.0ms	(/ (* 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))))
1.2s	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
26.0ms	(- (exp (* (+ a b) eps)) 1)

series2.5s

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
2.0s	(/ (* 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))))
284.0ms	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
87.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.7s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	4187
1	785
0	232

prune930.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

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

prune28.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize81.0ms

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

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

299.0ms	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
566.0ms	(/ (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))) (* eps (- (exp (* (+ a b) eps)) 1)))
1.4s	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
25.0ms	(- (exp (* (+ a b) eps)) 1)

series1.0s

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))
565.0ms	(/ (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))) (* eps (- (exp (* (+ a b) eps)) 1)))
291.0ms	(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
70.0ms	(- (exp (* (+ a b) eps)) 1)

simplify3.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5047
2	3639
1	742
0	222

prune825.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes170.0ms

Accuracy

0% (2.8b remaining)

Error of 3.2b against oracle of 0.4b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample19.3s

Algorithm

intervals

Results

6.7s	2619×	body	2560	valid
5.3s	3428×	body	1280	valid
4.6s	1908×	body	10240	exit
1.0s	1041×	body	640	valid
888.0ms	9909×	pre	80	true
262.0ms	339×	body	320	valid
109.0ms	427×	body	80	valid
77.0ms	147×	body	160	valid