Details

sample218.0ms

Algorithm

intervals

Results

67.0ms	56×	body	1280	valid
53.0ms	56×	body	10240	exit
41.0ms	335×	body	80	valid
14.0ms	25×	body	640	valid
8.0ms	19×	body	320	valid
3.0ms	13×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	2356
3	395
2	124
1	47
0	19

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out`

Counts

4 → 183

Calls

4 calls:

33.0ms	(* (- 1.0 eps) x)
53.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
83.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
51.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (- 1.0 eps) x)
67.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
81.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
292.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.5s

Counts

195 → 195

Iterations

Iter	Nodes
done	5001
1	1418
0	412

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* x x) x)
8.8b	(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* x x) 1.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`pow2` `expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `pow3` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 40

Calls

2 calls:

23.0ms	(* (* x x) x)
0.0ms	(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* x x) 1.0)))

series116.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(* (* x x) x)
54.0ms	(fma (* (* x x) x) 0.6666666666666667 (- 2.0 (* (* x x) 1.0)))

simplify1.1s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
2	1037
1	141
0	57

prune139.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (* x x) (- (* x 0.6666666666666667) 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-cbrt-cube` `prod-diff` `add-exp-log`
5×	`distribute-rgt-in` `add-sqr-sqrt` `distribute-lft-in`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/`
1×	`expm1-log1p-u` `flip3--` `associate-l` `*-commutative` `log1p-expm1-u` `flip--` `add-log-exp` `unswap-sqr`

Counts

1 → 33

Calls

1 calls:

44.0ms

(* (* x x) (- (* x 0.6666666666666667) 1.0))

series133.0ms

Counts

1 → 3

Calls

1 calls:

132.0ms

(* (* x x) (- (* x 0.6666666666666667) 1.0))

simplify2.0s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
2	2015
1	281
0	88

prune149.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 eps) 1.0)
0.0b	(* (- 1.0 eps) x)
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
4.1b	(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (- (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
49×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
13×	`fma-neg`
11×	`associate-l`
8×	`pow1` `add-cbrt-cube`
7×	`add-exp-log`
6×	`associate-r` `add-log-exp`
5×	`flip3--` `flip--` `difference-of-squares`
4×	`exp-neg` `expm1-log1p-u` `frac-times` `associate-*l/` `log1p-expm1-u` `div-inv`
3×	`neg-sub0` `exp-diff` `distribute-lft-out--`
2×	`pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `un-div-inv` `fma-udef`

Counts

4 → 135

Calls

4 calls:

35.0ms	(- (/ 1.0 eps) 1.0)
32.0ms	(* (- 1.0 eps) x)
90.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
1.0ms	(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (- (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (/ 1.0 eps) 1.0)
56.0ms	(* (- 1.0 eps) x)
93.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
283.0ms	(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (- (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))

simplify2.1s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	2423
1	571
0	240

prune941.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes84.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.0b

bsearch324.0ms

Steps

Iters	Range		Point
11	2.0412262699081644e-18	848.2985553752982	121.48694228142615

simplify9.0ms

Iterations

Iter	Nodes
done	58
2	58
1	48
0	29

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.0s	1887×	body	10240	exit
1.7s	1792×	body	1280	valid
1.3s	10003×	body	80	valid
1.3s	1206×	body	640	valid
197.0ms	622×	body	320	valid
67.0ms	338×	body	160	valid