Details

sample445.0ms

Algorithm

intervals

Results

139.0ms	88×	body	2560	valid
113.0ms	69×	body	10240	exit
97.0ms	110×	body	1280	valid
53.0ms	32×	body	640	valid
12.0ms	325×	pre	80	true
4.0ms	12×	body	320	valid
1.0ms	11×	body	80	valid
1.0ms	3×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ a b) eps)
5.1b	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
14.8b	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
18.2b	(/ eps (expm1 (* eps a)))

rewrite65.0ms

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:

21.0ms	(* (+ a b) eps)
23.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
8.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
8.0ms	(/ eps (expm1 (* eps a)))

series768.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (+ a b) eps)
587.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
100.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
56.0ms	(/ eps (expm1 (* eps a)))

simplify1.6s

Counts

150 → 150

Iterations

Iter	Nodes
done	5001
2	2039
1	584
0	220

prune833.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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:

23.0ms

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

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

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

simplify3.7s

Counts

38 → 38

Iterations

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

prune185.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ a b) 1)
0.0b	(expm1 (* eps a))
4.6b	(* (+ (/ a b) 1) (/ eps (expm1 (* eps a))))
18.2b	(/ eps (expm1 (* eps a)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
28×	`times-frac`
27×	`add-cube-cbrt`
13×	`fma-def` `associate-r`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `associate-l` `insert-posit16`
3×	`associate-/r` `flip3-+` `flip-+` `div-inv` `associate-/l`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `expm1-log1p` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `expm1-udef`

Counts

4 → 110

Calls

4 calls:

28.0ms	(+ (/ a b) 1)
0.0ms	(expm1 (* eps a))
93.0ms	(* (+ (/ a b) 1) (/ eps (expm1 (* eps a))))
7.0ms	(/ eps (expm1 (* eps a)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (/ a b) 1)
34.0ms	(expm1 (* eps a))
101.0ms	(* (+ (/ a b) 1) (/ eps (expm1 (* eps a))))
73.0ms	(/ eps (expm1 (* eps a)))

simplify1.5s

Counts

122 → 122

Iterations

Iter	Nodes
done	5006
2	1404
1	379
0	153

prune639.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt eps)
5.1b	(* (/ (expm1 (* (* (+ a b) (* (cbrt eps) (cbrt eps))) (cbrt eps))) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
14.8b	(/ (expm1 (* (* (+ a b) (* (cbrt eps) (cbrt eps))) (cbrt eps))) (expm1 (* eps b)))
18.2b	(/ eps (expm1 (* eps a)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
35×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l`
6×	`pow1` `cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`cbrt-prod`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow1/3` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `expm1-udef`

Counts

4 → 128

Calls

4 calls:

2.0ms	(cbrt eps)
32.0ms	(* (/ (expm1 (* (* (+ a b) (* (cbrt eps) (cbrt eps))) (cbrt eps))) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
5.0ms	(/ (expm1 (* (* (+ a b) (* (cbrt eps) (cbrt eps))) (cbrt eps))) (expm1 (* eps b)))
9.0ms	(/ eps (expm1 (* eps a)))

series1.2s

Counts

4 → 12

Calls

4 calls:

258.0ms	(cbrt eps)
721.0ms	(* (/ (expm1 (* (* (+ a b) (* (cbrt eps) (cbrt eps))) (cbrt eps))) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
142.0ms	(/ (expm1 (* (* (+ a b) (* (cbrt eps) (cbrt eps))) (cbrt eps))) (expm1 (* eps b)))
58.0ms	(/ eps (expm1 (* eps a)))

simplify2.0s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
2	1800
1	544
0	213

prune944.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes152.0ms

Accuracy

12.6% (3.0b remaining)

Error of 3.0b against oracle of 0.0b and baseline of 3.4b

bsearch145.0ms

Steps

Iters	Range		Point
5	-1.7298982814487828e-47	-8.228243517090271e-48	-9.609900552189287e-48

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	23

end0.0ms

sample15.9s

Algorithm

intervals

Results

4.9s	3439×	body	1280	valid
4.8s	2616×	body	2560	valid
3.5s	1972×	body	10240	exit
1.5s	1014×	body	640	valid
498.0ms	9976×	pre	80	true
206.0ms	341×	body	320	valid
53.0ms	462×	body	80	valid
31.0ms	132×	body	160	valid