Details

sample90.0ms

Algorithm

intervals

Results

40.0ms	107×	body	1280	valid
18.0ms	79×	body	640	valid
11.0ms	282×	body	80	valid
5.0ms	36×	body	320	valid
2.0ms	19×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	24	8
3	30	8
4	34	8
done	34	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.1b

localize8.0ms

Local error

Found 1 expressions with local error:

6.3b	(- (exp x) (exp (- x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

29.0ms

(- (exp x) (exp (- x)))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(- (exp x) (exp (- x)))

simplify2.7s

Counts

31 → 31

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	73	547
1	158	401
2	370	308
3	1377	253
done	5000	244

prune76.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

series80.0ms

Counts

1 → 3

Calls

1 calls:

80.0ms

(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

simplify903.0ms

Counts

13 → 13

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	26	218
1	50	212
2	148	186
3	837	186
done	5001	186

prune69.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
0.0b	(pow (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 3)
39.1b	(cbrt (pow (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 3))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

3 → 58

Calls

3 calls:

1.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
3.0ms	(pow (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 3)
3.0ms	(cbrt (pow (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 3))

series296.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
121.0ms	(pow (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 3)
92.0ms	(cbrt (pow (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 3))

simplify3.9s

Counts

67 → 67

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	92	1506
1	191	1292
2	533	1134
3	4214	1126
done	5000	1126

prune222.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp x) (exp (- x))))
6.5b	(- (exp (+ x x)) (exp (* x -2)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 103

Calls

3 calls:

14.0ms	(+ (exp x) (exp (- x)))
161.0ms	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp x) (exp (- x))))
84.0ms	(- (exp (+ x x)) (exp (* x -2)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (exp x) (exp (- x)))
112.0ms	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp x) (exp (- x))))
60.0ms	(- (exp (+ x x)) (exp (* x -2)))

simplify4.6s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	182	2456
1	430	2177
2	1181	1962
3	4911	1844
done	5000	1844

prune417.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

53.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.6b

bsearch52.0ms

Steps

Iters	Range		Point
8	-0.7718806003288846	-0.0008047768791668974	-0.012882299779342181

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	47
1	30	47
done	30	47

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.7s	3368×	body	1280	valid
721.0ms	2481×	body	640	valid
623.0ms	1250×	body	320	valid
566.0ms	8069×	body	80	valid
71.0ms	636×	body	160	valid