Details

sample115.0ms

Algorithm

intervals

Results

32.0ms	78×	body	10240	exit
30.0ms	61×	body	1280	valid
19.0ms	331×	body	80	valid
12.0ms	43×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	15×	body	160	valid

simplify559.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (100.0ms)

Iter	Nodes	Cost
0	19	29
1	47	29
2	124	29
3	334	27
4	1256	26
done	5001	26

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (- 1.0 eps) x)))
0.0b	(* (+ 1.0 eps) x)
0.0b	(exp (- (* (+ 1.0 eps) x)))
3.6b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
28×	`flip3--` `flip3-+` `flip--` `flip-+`
18×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 158

Calls

4 calls:

4.0ms	(exp (- (* (- 1.0 eps) x)))
9.0ms	(* (+ 1.0 eps) x)
3.0ms	(exp (- (* (+ 1.0 eps) x)))
29.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(exp (- (* (- 1.0 eps) x)))
26.0ms	(* (+ 1.0 eps) x)
29.0ms	(exp (- (* (+ 1.0 eps) x)))
192.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.7s

Counts

170 → 170

Iterations

Useful iterations: 2 (459.0ms)

Iter	Nodes	Cost
0	381	7574
1	1285	6798
2	4342	6366
done	5000	6366

prune429.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.6666666666666667 (pow x 3) 2.0)
4.8b	(- (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)))

series112.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
38.0ms	(- (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	454	468
3	2875	433
done	5000	430

prune113.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
4.8b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`associate-+r+`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-diff` `prod-exp`
2×	`pow1` `expm1-log1p-u` `sum-log` `log1p-expm1-u` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `fma-def` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 54

Calls

2 calls:

7.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

series75.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.6666666666666667 (pow x 3))
40.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

simplify427.0ms

Counts

60 → 60

Iterations

Useful iterations: done (425.0ms)

Iter	Nodes	Cost
0	98	684
1	247	603
2	903	558
done	5000	536

prune146.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

Local error

Found 4 expressions with local error:

4.8b	(+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) (- 2.0 (* 1.0 (pow x 2))))
41.0b	(cbrt (* 0.6666666666666667 (pow x 3)))
41.0b	(cbrt (* 0.6666666666666667 (pow x 3)))
41.0b	(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `associate-+r+` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `pow1/3` `prod-diff`
2×	`sum-log`
1×	`+-commutative` `associate-+r-` `sub-neg` `fma-def` `flip3-+` `diff-log` `flip-+`

Counts

4 → 54

Calls

4 calls:

18.0ms	(+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) (- 2.0 (* 1.0 (pow x 2))))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) (- 2.0 (* 1.0 (pow x 2))))
37.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
35.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
39.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

simplify1.4s

Counts

66 → 66

Iterations

Useful iterations: 3 (236.0ms)

Iter	Nodes	Cost
0	71	1126
1	181	1078
2	527	599
3	2970	566
done	5000	566

prune188.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes86.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.3b

bsearch128.0ms

Steps

Iters	Range		Point
8	1.1588875362171251	7686.007879781806	95.54164031582988

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	82
1	56	82
2	64	82
done	64	82

end0.0ms

sample2.9s

Algorithm

intervals

Results

806.0ms	1963×	body	10240	exit
783.0ms	1763×	body	1280	valid
561.0ms	9939×	body	80	valid
341.0ms	1288×	body	640	valid
105.0ms	614×	body	320	valid
37.0ms	338×	body	160	valid