Details

sample354.0ms

Algorithm

intervals

Results

159.0ms	86×	body	2560	valid
77.0ms	108×	body	1280	valid
58.0ms	49×	body	10240	exit
25.0ms	47×	body	640	valid
9.0ms	305×	pre	80	true
2.0ms	7×	body	320	valid
1.0ms	7×	body	80	valid
0.0ms	1×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3983
4	642
3	191
2	80
1	46
0	17

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ a b) eps)
3.7b	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
14.7b	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
17.3b	(/ eps (expm1 (* eps a)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
40×	`times-frac`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
17×	`associate-l`
16×	`associate-r`
8×	`pow1`
6×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-*l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative`
1×	`frac-times` `flip3-+` `div-sub` `associate-*r/` `flip-+` `distribute-lft-out` `expm1-udef`

Counts

4 → 138

Calls

4 calls:

22.0ms	(* (+ a b) eps)
39.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
6.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
6.0ms	(/ eps (expm1 (* eps a)))

series842.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ a b) eps)
640.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
111.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
65.0ms	(/ eps (expm1 (* eps a)))

simplify1.7s

Counts

150 → 150

Iterations

Iter	Nodes
done	5001
2	2039
1	584
0	220

prune840.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite45.0ms

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:

44.0ms

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

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify3.5s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
5	4603
4	1719
3	692
2	310
1	111
0	43

prune189.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/12 (* (* eps eps) a) (/ 1 a))
2.4b	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (fma -1/2 eps (fma 1/12 (* (* eps eps) a) (/ 1 a))))
5.1b	(* (* eps eps) a)
14.7b	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
16×	`add-cbrt-cube` `add-exp-log`
14×	`associate-l`
11×	`pow1`
6×	`associate-r`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `div-sub` `associate-*l/` `expm1-udef`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma 1/12 (* (* eps eps) a) (/ 1 a))
36.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (fma -1/2 eps (fma 1/12 (* (* eps eps) a) (/ 1 a))))
26.0ms	(* (* eps eps) a)
6.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma 1/12 (* (* eps eps) a) (/ 1 a))
367.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (fma -1/2 eps (fma 1/12 (* (* eps eps) a) (/ 1 a))))
22.0ms	(* (* eps eps) a)
92.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))

simplify2.1s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1433
1	445
0	185

prune751.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/12 (* (* eps eps) a) (/ 1 a))
2.2b	(* (+ (/ a b) 1) (fma -1/2 eps (fma 1/12 (* (* eps eps) a) (/ 1 a))))
5.1b	(* (* eps eps) a)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`associate-r` `add-cube-cbrt`
5×	`associate-l`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-l/` `-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `distribute-lft-out`

Counts

3 → 59

Calls

3 calls:

0.0ms	(fma 1/12 (* (* eps eps) a) (/ 1 a))
64.0ms	(* (+ (/ a b) 1) (fma -1/2 eps (fma 1/12 (* (* eps eps) a) (/ 1 a))))
33.0ms	(* (* eps eps) a)

series181.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma 1/12 (* (* eps eps) a) (/ 1 a))
113.0ms	(* (+ (/ a b) 1) (fma -1/2 eps (fma 1/12 (* (* eps eps) a) (/ 1 a))))
30.0ms	(* (* eps eps) a)

simplify3.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	3924
2	937
1	296
0	114

prune357.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes194.0ms

Accuracy

0% (3.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample15.6s

Algorithm

intervals

Results

5.9s	2646×	body	2560	valid
4.0s	3431×	body	1280	valid
3.0s	1880×	body	10240	exit
1.2s	1052×	body	640	valid
486.0ms	9882×	pre	80	true
382.0ms	121×	body	160	valid
186.0ms	415×	body	80	valid
160.0ms	337×	body	320	valid