Details

sample136.0ms

Algorithm

intervals

Results

78.0ms	66×	body	10240	exit
30.0ms	263×	body	80	valid
4.0ms	6×	body	640	valid
4.0ms	8×	body	320	valid
3.0ms	2×	body	1280	valid
2.0ms	6×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	26
3	26
2	22
1	15
0	8

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.5b	(log1p (exp x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-neg` `prod-diff`
2×	`pow1` `log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--`

Counts

2 → 34

Calls

2 calls:

11.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series161.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (log1p (exp x)) (* y x))
97.0ms	(log1p (exp x))

simplify1.8s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
3	3124
2	461
1	128
0	61

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* y x)))
1.1b	(cbrt (log1p (exp x)))
1.1b	(cbrt (log1p (exp x)))
1.1b	(cbrt (log1p (exp x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* y x)))
2.0ms	(cbrt (log1p (exp x)))
2.0ms	(cbrt (log1p (exp x)))
2.0ms	(cbrt (log1p (exp x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

364.0ms	(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* y x)))
231.0ms	(cbrt (log1p (exp x)))
270.0ms	(cbrt (log1p (exp x)))
300.0ms	(cbrt (log1p (exp x)))

simplify1.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	1947
2	413
1	132
0	68

prune362.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(log1p (exp x))
0.7b	(* (log1p (exp x)) (log1p (exp x)))
0.7b	(* (log1p (exp x)) (log1p (exp x)))
12.5b	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow3`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`difference-cubes` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-sub` `div-exp` `log1p-expm1` `flip-+` `div-inv` `flip--`

Counts

4 → 107

Calls

4 calls:

1.0ms	(log1p (exp x))
12.0ms	(* (log1p (exp x)) (log1p (exp x)))
12.0ms	(* (log1p (exp x)) (log1p (exp x)))
441.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(log1p (exp x))
89.0ms	(* (log1p (exp x)) (log1p (exp x)))
76.0ms	(* (log1p (exp x)) (log1p (exp x)))
219.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))

simplify3.0s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	2390
1	395
0	142

prune545.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize57.0ms

Local error

Found 4 expressions with local error:

1.1b	(cbrt (log1p (exp x)))
1.1b	(cbrt (log1p (exp x)))
1.1b	(cbrt (log1p (exp x)))
12.5b	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (* (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x)))) (* y x)))))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
9×	`cbrt-prod`
8×	`pow3`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `difference-cubes` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/r*` `pow1/3`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-sub` `div-exp` `flip-+` `div-inv` `flip--`

Counts

4 → 81

Calls

4 calls:

1.0ms	(cbrt (log1p (exp x)))
1.0ms	(cbrt (log1p (exp x)))
1.0ms	(cbrt (log1p (exp x)))
369.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (* (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x)))) (* y x)))))

series838.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt (log1p (exp x)))
234.0ms	(cbrt (log1p (exp x)))
215.0ms	(cbrt (log1p (exp x)))
189.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (* (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x)))) (* y x)))))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	2014
1	388
0	143

prune582.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes123.0ms

Accuracy

58% (0.5b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 1.5b

bsearch154.0ms

Steps

Iters	Range		Point
10	4.3052657707541446e-11	32.81305289360078	8.70864822876016e-07
6	-252269475.2976281	-15918868.771886915	-16179825.06434172

simplify11.0ms

Iterations

Iter	Nodes
done	32
2	32
1	30
0	22

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.3s	2386×	body	10240	exit
1.2s	8495×	body	80	valid
133.0ms	258×	body	640	valid
96.0ms	107×	body	1280	valid
72.0ms	202×	body	320	valid
18.0ms	90×	body	160	valid