Details

sample61.0ms

Algorithm

intervals

Results

17.0ms	37×	body	1280	valid
13.0ms	38×	body	640	valid
11.0ms	152×	body	80	valid
5.0ms	23×	body	320	valid
1.0ms	6×	body	160	valid

simplify12.7s

Counts

1 → 1

Iterations

Iter	Nodes
9	9494
8	1963
7	550
6	229
5	103
4	51
3	30
2	22
1	18
0	9

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* -2 x))))
0.0b	(+ 1 (exp (* -2 x)))
1.9b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
63×	`times-frac` `add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-cbrt-cube` `div-inv`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`expm1-def` `difference-of-sqr-1` `div-exp`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 150

Calls

3 calls:

14.0ms	(/ 2 (+ 1 (exp (* -2 x))))
12.0ms	(+ 1 (exp (* -2 x)))
119.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series130.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ 2 (+ 1 (exp (* -2 x))))
19.0ms	(+ 1 (exp (* -2 x)))
79.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify1.2s

Counts

159 → 159

Iterations

Iter	Nodes
3	2098
2	870
1	407
0	183

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1)
0.0b	(/ (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1) (+ (fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x))))))
0.0b	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
1.8b	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
76×	`times-frac`
61×	`add-sqr-sqrt`
49×	`add-cube-cbrt`
24×	`swap-sqr`
22×	`distribute-lft-out`
18×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
11×	`pow1`
10×	`associate-/r/`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv`
4×	`expm1-log1p-u` `associate-/r*` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
2×	`fma-udef`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 149

Calls

4 calls:

0.0ms	(fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1)
44.0ms	(/ (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1) (+ (fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x))))))
65.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
0.0ms	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

series972.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1)
303.0ms	(/ (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1) (+ (fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x))))))
51.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
556.0ms	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

simplify992.0ms

Counts

161 → 161

Iterations

Iter	Nodes
2	2062
1	707
0	243

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (log (exp (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1))) (+ (fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x))))))
0.0b	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
1.8b	(log (exp (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)))
1.8b	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
92×	`times-frac`
72×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
26×	`distribute-lft-out`
24×	`swap-sqr` `log-pow`
18×	`exp-prod` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
17×	`pow1`
10×	`associate-/r/`
7×	`associate-/l*`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log-prod` `associate-/r*` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 177

Calls

4 calls:

79.0ms	(/ (log (exp (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1))) (+ (fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x))))))
69.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
3.0ms	(log (exp (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)))
0.0ms	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

series568.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(/ (log (exp (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1))) (+ (fma (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x))))))
46.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
117.0ms	(log (exp (fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)))
96.0ms	(fma (/ 2 (+ 1 (exp (* -2 x)))) (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) -1)

simplify1.2s

Counts

189 → 189

Iterations

Iter	Nodes
2	2294
1	760
0	280

prune2.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ 1 (exp (* -2 x))))
0.4b	(cbrt (+ 1 (exp (* -2 x))))
0.4b	(/ 2 (cbrt (+ 1 (exp (* -2 x)))))
25.2b	(fma (/ 1 (* (cbrt (+ 1 (exp (* -2 x)))) (cbrt (+ 1 (exp (* -2 x)))))) (/ 2 (cbrt (+ 1 (exp (* -2 x))))) -1)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`cbrt-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
7×	`associate-/r*`
6×	`cbrt-div` `add-exp-log` `distribute-lft-out`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow1/3` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

4.0ms	(cbrt (+ 1 (exp (* -2 x))))
4.0ms	(cbrt (+ 1 (exp (* -2 x))))
11.0ms	(/ 2 (cbrt (+ 1 (exp (* -2 x)))))
0.0ms	(fma (/ 1 (* (cbrt (+ 1 (exp (* -2 x)))) (cbrt (+ 1 (exp (* -2 x)))))) (/ 2 (cbrt (+ 1 (exp (* -2 x))))) -1)

series896.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (+ 1 (exp (* -2 x))))
102.0ms	(cbrt (+ 1 (exp (* -2 x))))
194.0ms	(/ 2 (cbrt (+ 1 (exp (* -2 x)))))
469.0ms	(fma (/ 1 (* (cbrt (+ 1 (exp (* -2 x)))) (cbrt (+ 1 (exp (* -2 x)))))) (/ 2 (cbrt (+ 1 (exp (* -2 x))))) -1)

simplify866.0ms

Counts

105 → 105

Iterations

Iter	Nodes
3	2713
2	849
1	305
0	147

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes465.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.1b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	45
1	45
0	38

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.0s	1763×	body	1280	valid
951.0ms	1192×	body	640	valid
410.0ms	4116×	body	80	valid
193.0ms	621×	body	320	valid
55.0ms	308×	body	160	valid