Details

sample166.0ms

Algorithm

intervals

Results

96.0ms	82×	body	10240	exit
33.0ms	284×	body	80	valid
8.0ms	11×	body	640	valid
7.0ms	6×	body	1280	valid
2.0ms	6×	body	320	valid
1.0ms	2×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	26
3	26
2	22
1	15
0	8

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.7b	(log1p (exp x))

rewrite6.0ms

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:

5.0ms	(- (log1p (exp x)) (* y x))
0.0ms	(log1p (exp x))

series161.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(- (log1p (exp x)) (* y x))
78.0ms	(log1p (exp x))

simplify2.2s

Counts

40 → 40

Iterations

Iter	Nodes
4	2422
3	945
2	316
1	128
0	61

prune415.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.7b	(log1p (exp x))

rewrite11.0ms

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:

10.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series149.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(- (log1p (exp x)) (* y x))
70.0ms	(log1p (exp x))

simplify1.8s

Counts

40 → 40

Iterations

Iter	Nodes
4	2422
3	945
2	316
1	128
0	61

prune312.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize66.0ms

Local error

Found 4 expressions with local error:

0.7b	(log1p (exp x))
0.7b	(log1p (exp x))
0.7b	(log1p (exp x))
15.1b	(/ (- (* (* (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)))))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

1.0ms	(log1p (exp x))
1.0ms	(log1p (exp x))
1.0ms	(log1p (exp x))
354.0ms	(/ (- (* (* (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)))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(log1p (exp x))
50.0ms	(log1p (exp x))
63.0ms	(log1p (exp x))
217.0ms	(/ (- (* (* (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)))))

simplify3.5s

Counts

87 → 87

Iterations

Iter	Nodes
3	8226
2	1284
1	302
0	112

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize63.0ms

Local error

Found 4 expressions with local error:

10.8b	(/ (* (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x)))) (cbrt (- (* (* (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)))) (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))))
15.3b	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))
15.3b	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))
15.3b	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))

rewrite793.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
36×	`cbrt-prod`
35×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`associate-/r*`
22×	`cbrt-div`
18×	`pow3`
16×	`add-exp-log`
11×	`flip3--` `flip--`
10×	`add-cbrt-cube`
9×	`difference-cubes`
8×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
5×	`associate-/r/`
4×	`expm1-log1p-u` `frac-times` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `div-inv`
2×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

482.0ms	(/ (* (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x)))) (cbrt (- (* (* (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)))) (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))))
95.0ms	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))
86.0ms	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))
124.0ms	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ (* (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x)))) (cbrt (- (* (* (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)))) (cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))))
262.0ms	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))
281.0ms	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))
273.0ms	(cbrt (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))))

simplify1.4s

Counts

148 → 148

Iterations

Iter	Nodes
2	2261
1	705
0	247

prune2.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes90.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	7
1	7
0	6

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.3s	2415×	body	10240	exit
906.0ms	8361×	body	80	valid
477.0ms	124×	body	1280	valid
166.0ms	267×	body	640	valid
69.0ms	196×	body	320	valid
26.0ms	114×	body	160	valid