Details

sample116.0ms

Algorithm

intervals

Results

52.0ms	76×	body	10240	exit
32.0ms	270×	body	80	valid
3.0ms	8×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	2×	body	1280	valid
1.0ms	4×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.5b	(log (+ 1.0 (exp x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`pow1`
4×	`log-div` `fma-neg` `prod-diff` `associate--l+`
3×	`add-exp-log` `log-pow` `add-log-exp`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 45

Calls

2 calls:

10.0ms	(- (log (+ 1.0 (exp x))) (* x y))
5.0ms	(log (+ 1.0 (exp x)))

series163.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(- (log (+ 1.0 (exp x))) (* x y))
81.0ms	(log (+ 1.0 (exp x)))

simplify2.1s

Counts

51 → 51

Iterations

Iter	Nodes
done	5002
3	1626
2	509
1	209
0	94

prune328.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.0b	(sqrt (+ 1.0 (exp x)))
1.2b	(log (sqrt (+ 1.0 (exp x))))
1.2b	(log (sqrt (+ 1.0 (exp x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`log-prod`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `hypot-def`

Counts

4 → 82

Calls

4 calls:

8.0ms	(sqrt (+ 1.0 (exp x)))
8.0ms	(sqrt (+ 1.0 (exp x)))
7.0ms	(log (sqrt (+ 1.0 (exp x))))
12.0ms	(log (sqrt (+ 1.0 (exp x))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ 1.0 (exp x)))
57.0ms	(sqrt (+ 1.0 (exp x)))
146.0ms	(log (sqrt (+ 1.0 (exp x))))
170.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify3.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
4	4487
3	1305
2	452
1	174
0	90

prune562.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))
0.0b	(- (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))) (* x y))
5.3b	(fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

0.0ms	(fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))
9.0ms	(- (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))) (* x y))
1.0ms	(fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))

series525.0ms

Counts

3 → 9

Calls

3 calls:

321.0ms	(fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))
107.0ms	(- (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))) (* x y))
96.0ms	(fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))

simplify2.7s

Counts

50 → 50

Iterations

Iter	Nodes
done	5000
3	1961
2	479
1	160
0	75

prune302.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))))) (* x y))
0.8b	(exp (log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))))
5.1b	(log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))))
5.3b	(fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`exp-sum`
6×	`pow1` `fma-neg` `prod-diff` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-pow`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `fma-udef` `flip--` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

17.0ms	(- (exp (log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))))) (* x y))
3.0ms	(exp (log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))))
1.0ms	(log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))))
0.0ms	(fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (exp (log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))))) (* x y))
74.0ms	(exp (log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))))
192.0ms	(log (fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0))))
73.0ms	(fma x (fma 0.25 x 0.5) (fma -1/2 (* (/ x 2.0) (/ x 2.0)) (log 2.0)))

simplify2.3s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	3008
2	820
1	292
0	129

prune570.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes119.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	17

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.1s	2404×	body	10240	exit
607.0ms	8473×	body	80	valid
136.0ms	129×	body	1280	valid
103.0ms	239×	body	640	valid
51.0ms	98×	body	160	valid
45.0ms	178×	body	320	valid