Details

sample103.0ms

Algorithm

intervals

Results

54.0ms	82×	body	10240	exit
18.0ms	263×	body	80	valid
5.0ms	11×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	320	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
3	23
2	19
1	12
0	8

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 1 expressions with local error:

0.2b	(log (+ 1.0 (exp x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`add-sqr-sqrt` `pow1` `log-div` `add-exp-log` `add-cube-cbrt`
1×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `rem-log-exp` `log-pow` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 17

Calls

1 calls:

9.0ms

(log (+ 1.0 (exp x)))

series113.0ms

Counts

1 → 3

Calls

1 calls:

113.0ms

(log (+ 1.0 (exp x)))

simplify2.2s

Counts

20 → 20

Iterations

Iter	Nodes
done	5000
4	3855
3	941
2	276
1	109
0	54

prune116.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.5 x (fma (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))) (log 2.0)))
0.2b	(fma (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))) (log 2.0))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 0.5 x (fma (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))) (log 2.0)))
1.0ms	(fma (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))) (log 2.0))

series449.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(fma 0.5 x (fma (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))) (log 2.0)))
395.0ms	(fma (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))) (log 2.0))

simplify478.0ms

Counts

26 → 26

Iterations

Iter	Nodes
done	5001
3	702
2	160
1	61
0	38

prune235.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.5 x (expm1 (log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0)))))
0.2b	(fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0))
0.9b	(expm1 (log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0))))
7.8b	(log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`expm1-log1p-u`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 42

Calls

4 calls:

0.0ms	(fma 0.5 x (expm1 (log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0)))))
0.0ms	(fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0))
0.0ms	(expm1 (log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0))))
0.0ms	(log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

161.0ms	(fma 0.5 x (expm1 (log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0)))))
405.0ms	(fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0))
708.0ms	(expm1 (log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0))))
358.0ms	(log1p (fma (+ (/ -1/2 (* 2.0 2.0)) 0.25) (* x x) (log 2.0)))

simplify1.3s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
2	2076
1	482
0	175

prune455.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x x) (+ (log 2.0) 1))
0.4b	(fma 0.125 (/ (* x x) (+ (log 2.0) 1)) (log1p (log 2.0)))
1.0b	(pow (+ (log 2.0) 1) 2)
7.8b	(fma 0.0078125 (- (/ (pow x 4) (pow (+ (log 2.0) 1) 2))) (fma 0.125 (/ (* x x) (+ (log 2.0) 1)) (log1p (log 2.0))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt` `pow1` `add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/r*` `unpow-prod-down` `times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-pow`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `fma-udef`
1×	`pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*` `unpow2` `sqr-pow`

Counts

4 → 71

Calls

4 calls:

33.0ms	(/ (* x x) (+ (log 2.0) 1))
0.0ms	(fma 0.125 (/ (* x x) (+ (log 2.0) 1)) (log1p (log 2.0)))
10.0ms	(pow (+ (log 2.0) 1) 2)
0.0ms	(fma 0.0078125 (- (/ (pow x 4) (pow (+ (log 2.0) 1) 2))) (fma 0.125 (/ (* x x) (+ (log 2.0) 1)) (log1p (log 2.0))))

series1.9s

Counts

4 → 10

Calls

4 calls:

270.0ms	(/ (* x x) (+ (log 2.0) 1))
1.2s	(fma 0.125 (/ (* x x) (+ (log 2.0) 1)) (log1p (log 2.0)))
0.0ms	(pow (+ (log 2.0) 1) 2)
384.0ms	(fma 0.0078125 (- (/ (pow x 4) (pow (+ (log 2.0) 1) 2))) (fma 0.125 (/ (* x x) (+ (log 2.0) 1)) (log1p (log 2.0))))

simplify1.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	2113
1	341
0	124

prune625.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes100.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.0s	2439×	body	10240	exit
1.1s	8334×	body	80	valid
161.0ms	299×	body	640	valid
98.0ms	124×	body	1280	valid
53.0ms	199×	body	320	valid
19.0ms	111×	body	160	valid