Details

sample72.0ms

Algorithm

intervals

Results

21.0ms	45×	body	1280	valid
14.0ms	46×	body	640	valid
8.0ms	134×	body	80	valid
5.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3503
6	454
5	122
4	55
3	31
2	22
1	15
0	9

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
0.0b	(+ 1.0 (pow (exp x) -2.0))
0.0b	(pow (exp x) -2.0)
3.1b	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

32.0ms	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
16.0ms	(+ 1.0 (pow (exp x) -2.0))
7.0ms	(pow (exp x) -2.0)
178.0ms	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

series680.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ 2.0 (+ 1.0 (pow (exp x) -2.0)))
137.0ms	(+ 1.0 (pow (exp x) -2.0))
114.0ms	(pow (exp x) -2.0)
256.0ms	(- (/ 2.0 (+ 1.0 (pow (exp x) -2.0))) 1.0)

simplify1.0s

Counts

175 → 175

Iterations

Iter	Nodes
done	5002
2	1623
1	511
0	214

prune669.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp -2.0) x)
0.0b	(+ 1.0 (pow (exp -2.0) x))
3.0b	(log (exp (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)))
3.1b	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

rewrite483.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
112×	`add-sqr-sqrt`
108×	`prod-diff`
102×	`add-cube-cbrt`
86×	`times-frac`
59×	`log-prod`
56×	`exp-sum`
22×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
9×	`exp-prod`
8×	`flip3-+` `flip-+` `add-log-exp`
7×	`log-pow` `div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow` `unpow-prod-down` `fma-def`
2×	`sub-neg` `distribute-lft-out--`
1×	`pow-to-exp` `+-commutative` `log-div` `sum-log` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-exp` `flip--` `sqr-pow`

Counts

4 → 205

Calls

4 calls:

7.0ms	(pow (exp -2.0) x)
13.0ms	(+ 1.0 (pow (exp -2.0) x))
264.0ms	(log (exp (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)))
180.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

series392.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (exp -2.0) x)
52.0ms	(+ 1.0 (pow (exp -2.0) x))
143.0ms	(log (exp (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)))
162.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

simplify1.1s

Counts

217 → 217

Iterations

Iter	Nodes
done	5001
2	1799
1	618
0	321

prune967.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))
0.0b	(* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2)))
3.0b	(log (exp (- (/ 2.0 (+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))) 1.0)))
3.1b	(- (/ 2.0 (+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))) 1.0)

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
94×	`add-cube-cbrt`
90×	`prod-diff`
65×	`times-frac`
50×	`log-prod`
47×	`exp-sum`
18×	`unpow-prod-down`
15×	`fma-neg`
14×	`associate-/r/`
10×	`add-exp-log` `sqr-pow`
9×	`prod-exp` `unswap-sqr`
8×	`flip3-+` `flip-+` `add-log-exp`
7×	`swap-sqr` `associate-r` `associate-l` `log-pow` `div-inv`
6×	`pow-to-exp` `exp-prod` `add-cbrt-cube` `pow-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-def`
2×	`sub-neg` `distribute-lft-out--`
1×	`pow2` `+-commutative` `log-div` `sum-log` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--`

Counts

4 → 215

Calls

4 calls:

10.0ms	(+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))
43.0ms	(* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2)))
110.0ms	(log (exp (- (/ 2.0 (+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))) 1.0)))
72.0ms	(- (/ 2.0 (+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))) 1.0)

series552.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))
71.0ms	(* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2)))
206.0ms	(log (exp (- (/ 2.0 (+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))) 1.0)))
198.0ms	(- (/ 2.0 (+ 1.0 (* (pow (exp -2.0) (/ x 2)) (pow (exp -2.0) (/ x 2))))) 1.0)

simplify2.1s

Counts

227 → 227

Iterations

Iter	Nodes
done	5001
2	2475
1	704
0	359

prune980.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
8.4b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`unpow-prod-down` `add-cbrt-cube` `cube-prod` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 43

Calls

2 calls:

20.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series239.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(* 0.33333333333333337 (pow x 3))
190.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify3.9s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
3	4457
2	585
1	159
0	70

prune277.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes170.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.6b

bsearch165.0ms

Steps

Iters	Range		Point
8	7.294142785006675e-07	0.003512390648898176	0.0008133336636844119
7	-0.00181011214377754	-0.00010545444661221848	-0.000929047538918183

simplify7.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample2.0s

Algorithm

intervals

Results

786.0ms	1768×	body	1280	valid
482.0ms	1235×	body	640	valid
262.0ms	4058×	body	80	valid
110.0ms	626×	body	320	valid
36.0ms	313×	body	160	valid