Details

sample456.0ms

Algorithm

intervals

Results

167.0ms	80×	body	2560	valid
113.0ms	95×	body	1280	valid
79.0ms	48×	body	10240	exit
56.0ms	45×	body	640	valid
13.0ms	304×	pre	80	true
5.0ms	9×	body	320	valid
4.0ms	22×	body	80	valid
1.0ms	5×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* (+ a b) eps))
0.1b	(* (expm1 (* (+ a b) eps)) eps)
0.3b	(* (expm1 (* eps b)) (expm1 (* eps a)))
36.2b	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))

rewrite27.0ms

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))
5.0ms	(* (expm1 (* (+ a b) eps)) eps)
6.0ms	(* (expm1 (* eps b)) (expm1 (* eps a)))
15.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))

series898.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(expm1 (* (+ a b) eps))
170.0ms	(* (expm1 (* (+ a b) eps)) eps)
82.0ms	(* (expm1 (* eps b)) (expm1 (* eps a)))
579.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	2001
3	2001
2	1711
1	346
0	137

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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:

11.0ms

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

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify1.1s

Counts

38 → 38

Iterations

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

prune228.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
0.5b	(cbrt (/ 1 a))
0.5b	(cbrt (/ 1 a))
0.5b	(cbrt (/ 1 a))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 165

Calls

4 calls:

11.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
1.0ms	(cbrt (/ 1 a))
1.0ms	(cbrt (/ 1 a))
2.0ms	(cbrt (/ 1 a))

series979.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
223.0ms	(cbrt (/ 1 a))
250.0ms	(cbrt (/ 1 a))
262.0ms	(cbrt (/ 1 a))

simplify947.0ms

Counts

177 → 177

Iterations

Iter	Nodes
done	2000
4	2000
3	1286
2	504
1	254
0	145

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* (+ a b) eps))
4.6b	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
12.3b	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
16.2b	(/ eps (expm1 (* eps a)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
34×	`*-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`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `div-inv` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `expm1-udef`
1×	`frac-times` `expm1-log1p` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 126

Calls

4 calls:

0.0ms	(expm1 (* (+ a b) eps))
18.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
4.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
4.0ms	(/ eps (expm1 (* eps a)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(expm1 (* (+ a b) eps))
515.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
89.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
48.0ms	(/ eps (expm1 (* eps a)))

simplify1.1s

Counts

138 → 138

Iterations

Iter	Nodes
done	2003
3	2003
2	1709
1	515
0	197

prune1.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes162.0ms

Accuracy

-19.5% (3.8b remaining)

Error of 3.8b against oracle of 0.0b and baseline of 3.2b

bsearch632.0ms

Steps

Iters	Range		Point
9	3.6595324496438e+242	3.152833417898111e+248	2.937678032680349e+248
6	2.639049132307619e+137	2.664833580651828e+138	8.414834018041844e+137

simplify5.0ms

Iterations

Iter	Nodes
done	34
1	34
0	24

end0.0ms

sample18.4s

Algorithm

intervals

Results

5.6s	2494×	body	2560	valid
5.3s	1940×	body	10240	exit
4.8s	3464×	body	1280	valid
993.0ms	1131×	body	640	valid
867.0ms	9942×	pre	80	true
328.0ms	342×	body	320	valid
71.0ms	426×	body	80	valid
55.0ms	145×	body	160	valid