Details

sample113.0ms

Algorithm

intervals

Results

46.0ms	100×	body	1280	valid
25.0ms	82×	body	640	valid
11.0ms	256×	body	80	valid
9.0ms	45×	body	320	valid
2.0ms	18×	body	160	valid

simplify28.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.8b

localize14.0ms

Local error

Found 1 expressions with local error:

5.6b	(- (exp x) (exp (- x)))

rewrite35.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

33.0ms

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

series55.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

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

simplify669.0ms

Counts

31 → 31

Iterations

Useful iterations: done (668.0ms)

Iter	Nodes	Cost
0	73	547
1	170	404
2	671	308
done	5001	254

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 2 x (fma 1/3 (pow x 3) (* 1/60 (pow x 5))))
0.1b	(* 1/60 (pow x 5))
0.1b	(fma 1/3 (pow x 3) (* 1/60 (pow x 5)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

0.0ms	(fma 2 x (fma 1/3 (pow x 3) (* 1/60 (pow x 5))))
18.0ms	(* 1/60 (pow x 5))
1.0ms	(fma 1/3 (pow x 3) (* 1/60 (pow x 5)))

series393.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(fma 2 x (fma 1/3 (pow x 3) (* 1/60 (pow x 5))))
78.0ms	(* 1/60 (pow x 5))
209.0ms	(fma 1/3 (pow x 3) (* 1/60 (pow x 5)))

simplify1.5s

Counts

56 → 56

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	79	619
1	161	581
2	476	529
3	2433	529
done	5000	529

prune281.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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)))
5.5b	(- (exp (+ x x)) (exp (* x -2)))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
24×	`times-frac` `add-cube-cbrt`
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-cbrt-cube` `add-exp-log`
4×	`associate-/r*` `fma-neg`
3×	`expm1-log1p-u` `pow1` `fma-def` `log1p-expm1-u`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 103

Calls

3 calls:

25.0ms	(+ (exp (- x)) (exp x))
167.0ms	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp (- x)) (exp x)))
60.0ms	(- (exp (+ x x)) (exp (* x -2)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (exp (- x)) (exp x))
98.0ms	(/ (- (exp (+ x x)) (exp (* x -2))) (+ (exp (- x)) (exp x)))
73.0ms	(- (exp (+ x x)) (exp (* x -2)))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	183	2456
1	458	2180
2	2085	1964
done	5000	1908

prune553.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x))))
0.0b	(pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x)))) 3)
0.1b	(cbrt (pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x)))) 3))
5.5b	(- (exp (* 2 x)) (exp (* -2 x)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

160×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
100×	`times-frac`
64×	`add-cube-cbrt`
58×	`cbrt-prod`
52×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`add-cbrt-cube` `prod-diff` `add-exp-log`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg`
2×	`cube-div` `cube-mult` `cbrt-undiv` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `rem-cube-cbrt` `sqr-pow` `associate-/l/`
1×	`pow-to-exp` `cbrt-div` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `rem-cbrt-cube`

Counts

4 → 220

Calls

4 calls:

65.0ms	(/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x))))
64.0ms	(pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x)))) 3)
45.0ms	(cbrt (pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x)))) 3))
14.0ms	(- (exp (* 2 x)) (exp (* -2 x)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x))))
129.0ms	(pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x)))) 3)
124.0ms	(cbrt (pow (/ (- (exp (* 2 x)) (exp (* -2 x))) (+ (exp x) (exp (- x)))) 3))
54.0ms	(- (exp (* 2 x)) (exp (* -2 x)))

simplify2.3s

Counts

232 → 232

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	264	7033
1	881	6183
2	4847	5725
done	5000	5693

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	14	15
done	14	15

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.3s	3453×	body	1280	valid
1.0s	2426×	body	640	valid
426.0ms	8001×	body	80	valid
392.0ms	1235×	body	320	valid
72.0ms	607×	body	160	valid