Details

sample512.0ms

Algorithm

intervals

Results

204.0ms	74×	body	2560	valid
119.0ms	102×	body	1280	valid
110.0ms	58×	body	10240	exit
32.0ms	43×	body	640	valid
14.0ms	314×	pre	80	true
5.0ms	10×	body	320	valid
4.0ms	22×	body	80	valid
2.0ms	5×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
5	3964
4	642
3	191
2	80
1	46
0	17

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (* (+ a b) eps))
5.5b	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
11.5b	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
14.7b	(/ eps (expm1 (* eps a)))

rewrite24.0ms

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))
14.0ms	(* (/ (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)))

series904.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(expm1 (* (+ a b) eps))
663.0ms	(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
116.0ms	(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
50.0ms	(/ eps (expm1 (* eps a)))

simplify2.5s

Counts

138 → 138

Iterations

Iter	Nodes
3	6104
2	1605
1	510
0	197

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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:

12.0ms

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

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

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

simplify2.4s

Counts

38 → 38

Iterations

Iter	Nodes
5	3732
4	1553
3	687
2	313
1	109
0	43

prune387.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

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))

rewrite43.0ms

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:

25.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
7.0ms	(cbrt (/ 1 a))
3.0ms	(cbrt (/ 1 a))
3.0ms	(cbrt (/ 1 a))

series1.2s

Counts

4 → 12

Calls

4 calls:

326.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
316.0ms	(cbrt (/ 1 a))
318.0ms	(cbrt (/ 1 a))
226.0ms	(cbrt (/ 1 a))

simplify2.0s

Counts

177 → 177

Iterations

Iter	Nodes
4	4154
3	1185
2	473
1	249
0	145

prune2.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1 a))
0.5b	(cbrt (/ 1 a))
0.5b	(cbrt (/ 1 a))
5.0b	(exp (log (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`pow1` `exp-prod`
9×	`pow1/3` `log-pow`
7×	`cbrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `exp-diff` `div-inv`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `log-prod` `pow-plus` `exp-sum` `associate-l/` `associate-r/` `rem-exp-log`

Counts

4 → 102

Calls

4 calls:

1.0ms	(cbrt (/ 1 a))
1.0ms	(cbrt (/ 1 a))
1.0ms	(cbrt (/ 1 a))
23.0ms	(exp (log (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

227.0ms	(cbrt (/ 1 a))
274.0ms	(cbrt (/ 1 a))
258.0ms	(cbrt (/ 1 a))
321.0ms	(exp (log (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))))

simplify2.9s

Counts

114 → 114

Iterations

Iter	Nodes
5	5102
4	1423
3	622
2	307
1	183
0	113

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes218.0ms

Accuracy

16.7% (2.8b remaining)

Error of 2.8b against oracle of 0.0b and baseline of 3.4b

bsearch344.0ms

Steps

Iters	Range		Point
5	2.685963425170424e-72	5.795394238713599e-72	5.71803006796694e-72
4	-7.853274069490719e-75	-4.3186758349832207e-75	-7.739597797624075e-75

simplify9.0ms

Iterations

Iter	Nodes
2	34
1	34
0	23

end0.0ms

sample18.4s

Algorithm

intervals

Results

6.5s	2610×	body	2560	valid
5.0s	3408×	body	1280	valid
4.7s	2104×	body	10240	exit
916.0ms	1088×	body	640	valid
609.0ms	10106×	pre	80	true
172.0ms	320×	body	320	valid
111.0ms	453×	body	80	valid
66.0ms	123×	body	160	valid