Details

sample505.0ms

Algorithm

intervals

Results

185.0ms	80×	body	2560	valid
117.0ms	95×	body	1280	valid
90.0ms	48×	body	10240	exit
37.0ms	45×	body	640	valid
32.0ms	22×	body	80	valid
16.0ms	304×	pre	80	true
5.0ms	9×	body	320	valid
2.0ms	5×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
5	3998
4	640
3	189
2	78
1	44
0	17

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* (+ a b) eps))
7.8b	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
16.3b	(/ eps (expm1 (* eps b)))
16.5b	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

1.0ms	(expm1 (* (+ a b) eps))
21.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
9.0ms	(/ eps (expm1 (* eps b)))
30.0ms	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(expm1 (* (+ a b) eps))
134.0ms	(* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps)))
57.0ms	(/ eps (expm1 (* eps b)))
270.0ms	(/ (* (/ eps (expm1 (* eps b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

simplify8.8s

Counts

116 → 116

Iterations

Iter	Nodes
3	7238
2	1551
1	416
0	173

prune694.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

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:

26.0ms

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

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify1.4s

Counts

38 → 38

Iterations

Iter	Nodes
4	2780
3	1109
2	412
1	107
0	43

prune158.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (fma eps b (* a eps)))
4.4b	(/ (/ (expm1 (* a eps)) eps) (/ (expm1 (fma eps b (* a eps))) (expm1 (* eps b))))
12.3b	(/ (expm1 (fma eps b (* a eps))) (expm1 (* eps b)))
16.2b	(/ (expm1 (* a eps)) eps)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

439×	`times-frac`
216×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
31×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/r` `associate-/l`
10×	`cbrt-undiv` `div-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `expm1-udef` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`expm1-log1p` `associate-/r/` `associate-/l/`

Counts

4 → 293

Calls

4 calls:

1.0ms	(expm1 (fma eps b (* a eps)))
18.0ms	(/ (/ (expm1 (* a eps)) eps) (/ (expm1 (fma eps b (* a eps))) (expm1 (* eps b))))
8.0ms	(/ (expm1 (fma eps b (* a eps))) (expm1 (* eps b)))
9.0ms	(/ (expm1 (* a eps)) eps)

series507.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(expm1 (fma eps b (* a eps)))
287.0ms	(/ (/ (expm1 (* a eps)) eps) (/ (expm1 (fma eps b (* a eps))) (expm1 (* eps b))))
109.0ms	(/ (expm1 (fma eps b (* a eps))) (expm1 (* eps b)))
63.0ms	(/ (expm1 (* a eps)) eps)

simplify5.6s

Counts

305 → 305

Iterations

Iter	Nodes
2	4981
1	1527
0	501

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/12 (* (* eps eps) b) (/ 1 b))
6.1b	(* (* eps eps) b)
7.5b	(* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps)))
15.5b	(/ (* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma 1/12 (* (* eps eps) b) (/ 1 b))
25.0ms	(* (* eps eps) b)
6.0ms	(* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps)))
9.0ms	(/ (* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma 1/12 (* (* eps eps) b) (/ 1 b))
21.0ms	(* (* eps eps) b)
127.0ms	(* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps)))
296.0ms	(/ (* (fma -1/2 eps (fma 1/12 (* (* eps eps) b) (/ 1 b))) (expm1 (* (+ a b) eps))) (expm1 (* eps a)))

simplify4.0s

Counts

90 → 90

Iterations

Iter	Nodes
3	5480
2	1187
1	371
0	157

prune555.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

-22.7% (3.9b remaining)

Error of 3.9b against oracle of 0.0b and baseline of 3.2b

bsearch706.0ms

Steps

Iters	Range		Point
9	3.6595324496438e+242	3.152833417898111e+248	2.335242954070617e+248
5	5.559383257856542e+122	2.1749718142746195e+123	1.1199581729972231e+123

simplify9.0ms

Iterations

Iter	Nodes
2	29
1	29
0	23

end0.0ms

sample19.7s

Algorithm

intervals

Results

5.9s	3464×	body	1280	valid
5.8s	2494×	body	2560	valid
4.9s	1940×	body	10240	exit
1.4s	1131×	body	640	valid
1.0s	9942×	pre	80	true
265.0ms	342×	body	320	valid
87.0ms	145×	body	160	valid
75.0ms	426×	body	80	valid