Details

sample93.0ms

Algorithm

intervals

Results

24.0ms	63×	body	10240	exit
19.0ms	47×	body	1280	valid
17.0ms	338×	body	80	valid
13.0ms	39×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	12×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (146.0ms)

Iter	Nodes	Cost
0	19	29
1	47	29
2	124	29
3	323	27
4	1091	26
5	4644	26
done	5000	26

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (+ 1.0 eps) x)))
0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
2.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
73×	`exp-neg`
72×	`frac-times`
55×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
18×	`un-div-inv`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt` `associate-l`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`exp-prod` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `fma-neg` `diff-log` `prod-diff` `neg-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 163

Calls

4 calls:

3.0ms	(exp (- (* (+ 1.0 eps) x)))
10.0ms	(* (+ 1.0 eps) x)
10.0ms	(* (- 1.0 eps) x)
27.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(exp (- (* (+ 1.0 eps) x)))
26.0ms	(* (+ 1.0 eps) x)
29.0ms	(* (- 1.0 eps) x)
189.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.3s

Counts

175 → 175

Iterations

Useful iterations: 2 (478.0ms)

Iter	Nodes	Cost
0	390	7605
1	1255	6831
2	4064	6400
done	5001	6400

prune421.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.6666666666666667 (pow x 3) 2.0)
6.8b	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite4.0ms

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)
3.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series113.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
40.0ms	(- (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	120	518
2	420	468
3	2482	433
done	5001	430

prune104.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.6666666666666667 (pow x 3) 2.0)
0.5b	(exp (log (fma 0.6666666666666667 (pow x 3) 2.0)))
6.8b	(- (exp (log (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))
10.9b	(log (fma 0.6666666666666667 (pow x 3) 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
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` `flip--` `fma-udef` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

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

series463.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
75.0ms	(exp (log (fma 0.6666666666666667 (pow x 3) 2.0)))
42.0ms	(- (exp (log (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))
274.0ms	(log (fma 0.6666666666666667 (pow x 3) 2.0))

simplify1.9s

Counts

79 → 79

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	123	1160
1	259	1010
2	798	886
3	4313	846
done	5000	840

prune235.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0))))
0.5b	(exp (expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0)))))
6.8b	(- (exp (expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0))))) (* 1.0 (pow x 2)))
10.9b	(log (fma 0.6666666666666667 (pow x 3) 2.0))

rewrite11.0ms

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×	`expm1-udef`
1×	`sub-neg` `expm1-log1p` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `log-pow` `flip--` `rem-exp-log`

Counts

4 → 59

Calls

4 calls:

0.0ms	(expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0))))
1.0ms	(exp (expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0)))))
8.0ms	(- (exp (expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0))))) (* 1.0 (pow x 2)))
1.0ms	(log (fma 0.6666666666666667 (pow x 3) 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

663.0ms	(expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0))))
806.0ms	(exp (expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0)))))
211.0ms	(- (exp (expm1 (log1p (log (fma 0.6666666666666667 (pow x 3) 2.0))))) (* 1.0 (pow x 2)))
274.0ms	(log (fma 0.6666666666666667 (pow x 3) 2.0))

simplify532.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (164.0ms)

Iter	Nodes	Cost
0	181	1448
1	456	1210
2	1574	1102
done	5000	1102

prune271.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes133.0ms

Accuracy

96.7% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 17.1b

bsearch148.0ms

Steps

Iters	Range		Point
10	1.1679697638036715e-17	38.74833267440093	33.94148395765872

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	61
1	46	61
2	48	61
done	48	61

end0.0ms

sample2.7s

Algorithm

intervals

Results

753.0ms	1900×	body	10240	exit
720.0ms	1697×	body	1280	valid
526.0ms	10134×	body	80	valid
310.0ms	1259×	body	640	valid
107.0ms	650×	body	320	valid
35.0ms	327×	body	160	valid