Details

sample194.0ms

Algorithm

intervals

Results

62.0ms	52×	body	10240	exit
36.0ms	43×	body	1280	valid
36.0ms	327×	body	80	valid
20.0ms	44×	body	640	valid
5.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	19	29
1	71	29
2	2386	27
done	5000	27

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (- 1.0 eps) x))
0.3b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.3b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
1.5b	(- (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite444.0ms

Algorithm

rewrite-expression-head

Rules

658×	`times-frac`
640×	`add-sqr-sqrt` `*-un-lft-identity`
368×	`add-cube-cbrt`
352×	`prod-diff`
108×	`difference-of-squares`
75×	`distribute-lft-out`
59×	`distribute-lft-out--`
41×	`div-inv`
16×	`fma-neg`
10×	`associate-/l*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`add-exp-log` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `flip3--` `exp-to-pow` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `flip--`
1×	`sub-neg` `exp-prod` `flip3-+` `frac-sub` `flip-+` `rem-exp-log` `associate--r-`

Counts

4 → 485

Calls

4 calls:

9.0ms	(exp (* (- 1.0 eps) x))
60.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
67.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
243.0ms	(- (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(exp (* (- 1.0 eps) x))
61.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
91.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
273.0ms	(- (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.7s

Counts

497 → 497

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	550	43442
done	5000	34851

prune2.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.6666666666666667 (pow x 3) 2.0)
6.2b	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

0.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
10.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series181.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
56.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify1.5s

Counts

37 → 37

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	53	544
1	330	509
done	5000	470

prune140.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.6666666666666667 (pow x 3) 2.0)
0.4b	(exp (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))))
6.2b	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
11.2b	(log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
6.0ms	(exp (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))))
6.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
8.0ms	(log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
47.0ms	(exp (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))))
74.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
136.0ms	(log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

simplify1.4s

Counts

78 → 78

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	124	1432
1	651	1284
done	5000	1173

prune448.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log1p (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))))
0.4b	(exp (expm1 (log1p (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))))))
6.2b	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
11.2b	(log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(expm1 (log1p (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))))
3.0ms	(exp (expm1 (log1p (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))))))
6.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
5.0ms	(log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

series796.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(expm1 (log1p (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))))
312.0ms	(exp (expm1 (log1p (log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))))))
60.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))
151.0ms	(log (- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2))))

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	151	1558
1	892	1415
done	5001	1230

prune471.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

regimes176.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.5b

bsearch213.0ms

Steps

Iters	Range		Point
9	0.12160444842987421	18133.886566758163	356.35535311208105

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	77
1	40	77
done	40	77

end0.0ms

sample9.5s

Algorithm

intervals

Results

2.5s	1975×	body	10240	exit
2.5s	9978×	body	80	valid
2.1s	1747×	body	1280	valid
1.3s	1239×	body	640	valid
329.0ms	647×	body	320	valid
71.0ms	316×	body	160	valid