Details

sample629.0ms

Algorithm

intervals

Results

264.0ms	85×	body	2560	valid
147.0ms	105×	body	1280	valid
129.0ms	54×	body	10240	exit
35.0ms	38×	body	640	valid
16.0ms	310×	pre	80	true
7.0ms	10×	body	320	valid
3.0ms	6×	body	160	valid
3.0ms	12×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
5	2002
4	642
3	191
2	80
1	46
0	17

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* (+ a b) eps))
0.1b	(* (expm1 (* eps b)) (expm1 (* eps a)))
0.1b	(* (expm1 (* (+ a b) eps)) eps)
38.8b	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `*-commutative` `unswap-sqr`
1×	`expm1-log1p` `clear-num` `associate-/r` `frac-2neg` `times-frac` `div-inv` `associate-/l` `expm1-udef`

Counts

4 → 78

Calls

4 calls:

0.0ms	(expm1 (* (+ a b) eps))
6.0ms	(* (expm1 (* eps b)) (expm1 (* eps a)))
7.0ms	(* (expm1 (* (+ a b) eps)) eps)
22.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))

series820.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(expm1 (* (+ a b) eps))
56.0ms	(* (expm1 (* eps b)) (expm1 (* eps a)))
133.0ms	(* (expm1 (* (+ a b) eps)) eps)
558.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	2001
3	2001
2	1718
1	346
0	137

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`

Counts

1 → 35

Calls

1 calls:

24.0ms

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

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

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

simplify1.0s

Counts

38 → 38

Iterations

Iter	Nodes
done	2004
5	2004
4	1719
3	692
2	310
1	111
0	43

prune315.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

12.6b

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

rewrite28.0ms

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×	`expm1-log1p-u` `pow1` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

28.0ms

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

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

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

simplify1.1s

Counts

31 → 31

Iterations

Iter	Nodes
done	2055
4	2055
3	1636
2	476
1	148
0	58

prune242.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ a b) a)
8.3b	(/ (/ (+ a b) a) b)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
92×	`*-un-lft-identity`
60×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`associate-/l*`
16×	`distribute-lft-out`
9×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`flip3-+` `flip-+`

Counts

2 → 121

Calls

2 calls:

21.0ms	(/ (+ a b) a)
32.0ms	(/ (/ (+ a b) a) b)

series87.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ (+ a b) a)
55.0ms	(/ (/ (+ a b) a) b)

simplify866.0ms

Counts

127 → 127

Iterations

Iter	Nodes
done	2016
3	2016
2	1023
1	388
0	172

prune996.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes150.0ms

Accuracy

11% (2.8b remaining)

Error of 2.8b against oracle of 0.0b and baseline of 3.1b

bsearch236.0ms

Steps

Iters	Range		Point
6	-2.3035659761929849e-38	-4.667900972040201e-39	-7.922516355979929e-39

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	20

end0.0ms

sample18.3s

Algorithm

intervals

Results

6.2s	2545×	body	2560	valid
5.2s	3487×	body	1280	valid
4.4s	1929×	body	10240	exit
911.0ms	1063×	body	640	valid
617.0ms	362×	body	320	valid
467.0ms	9931×	pre	80	true
81.0ms	134×	body	160	valid
71.0ms	411×	body	80	valid