Details

sample184.0ms

Algorithm

intervals

Results

66.0ms	61×	body	10240	exit
36.0ms	55×	body	1280	valid
30.0ms	325×	body	80	valid
17.0ms	38×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	12×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (277.0ms)

Iter	Nodes	Cost
0	19	29
1	47	29
2	124	29
3	353	27
4	1008	26
5	4514	26
done	5000	26

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (- 1.0 eps) x)))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(exp (- (* (+ 1.0 eps) x)))
3.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
31×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
19×	`un-div-inv`
15×	`add-sqr-sqrt`
12×	`exp-prod`
10×	`*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `associate-l` `add-cbrt-cube`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log` `difference-of-squares`
1×	`sub-neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 167

Calls

4 calls:

12.0ms	(exp (- (* (- 1.0 eps) x)))
108.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
7.0ms	(exp (- (* (+ 1.0 eps) x)))
87.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp (- (* (- 1.0 eps) x)))
63.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
49.0ms	(exp (- (* (+ 1.0 eps) x)))
355.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify2.8s

Counts

179 → 179

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	382	8008
1	1069	7178
2	3746	6719
done	5000	6649

prune677.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.6666666666666667 (pow x 3) 2.0)
7.4b	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite8.0ms

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

series152.0ms

Counts

2 → 6

Calls

2 calls:

107.0ms	(fma 0.6666666666666667 (pow x 3) 2.0)
45.0ms	(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify3.5s

Counts

37 → 37

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	53	544
1	119	518
2	387	468
3	2205	433
done	5000	386

prune204.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

7.4b	(fma (* (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (- (* 1.0 (pow x 2))))
12.3b	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
12.3b	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
12.3b	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series2.8s

Counts

4 → 12

Calls

4 calls:

402.0ms	(fma (* (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (- (* 1.0 (pow x 2))))
1.0s	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
700.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
645.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

simplify1.9s

Counts

61 → 61

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	126	1526
1	296	1478
2	960	1209
3	4333	995
done	5000	989

prune344.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(* 0.07407407407407407 (cbrt (/ 1 (pow 2.0 5))))
12.3b	(fma (fma (pow x 3) 0.1111111111111111 1) (cbrt 2.0) (* (pow x 6) (- (* (cbrt 2.0) 0.006172839506172839) (* 0.07407407407407407 (cbrt (/ 1 (pow 2.0 5)))))))
12.3b	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
12.3b	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`cbrt-prod`
28×	`associate-r`
27×	`times-frac`
25×	`*-un-lft-identity`
22×	`add-cube-cbrt`
11×	`unpow-prod-down`
8×	`unswap-sqr`
6×	`pow1` `add-exp-log`
5×	`add-cbrt-cube` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`pow1/3`
1×	`cbrt-div` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 89

Calls

4 calls:

38.0ms	(* 0.07407407407407407 (cbrt (/ 1 (pow 2.0 5))))
0.0ms	(fma (fma (pow x 3) 0.1111111111111111 1) (cbrt 2.0) (* (pow x 6) (- (* (cbrt 2.0) 0.006172839506172839) (* 0.07407407407407407 (cbrt (/ 1 (pow 2.0 5)))))))
11.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
1.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

series1.8s

Counts

4 → 10

Calls

4 calls:

0.0ms	(* 0.07407407407407407 (cbrt (/ 1 (pow 2.0 5))))
512.0ms	(fma (fma (pow x 3) 0.1111111111111111 1) (cbrt 2.0) (* (pow x 6) (- (* (cbrt 2.0) 0.006172839506172839) (* 0.07407407407407407 (cbrt (/ 1 (pow 2.0 5)))))))
614.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
665.0ms	(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

simplify2.7s

Counts

99 → 99

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	235	1775
1	465	1642
2	1139	1518
3	4736	1399
done	5000	1397

prune791.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes151.0ms

Accuracy

90.7% (1.6b remaining)

Error of 2.0b against oracle of 0.4b and baseline of 17.2b

bsearch235.0ms

Steps

Iters	Range		Point
8	2.1318049287245128e-27	3.447572751372202e-23	3.375282683015706e-23

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	53
1	41	53
2	43	53
done	43	53

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.7s	2007×	body	10240	exit
2.6s	1653×	body	1280	valid
1.9s	10148×	body	80	valid
680.0ms	1247×	body	640	valid
305.0ms	618×	body	320	valid
82.0ms	347×	body	160	valid