Details

sample128.0ms

Algorithm

intervals

Results

48.0ms	96×	body	1280	valid
31.0ms	97×	body	640	valid
16.0ms	323×	body	80	valid
7.0ms	33×	body	320	valid
2.0ms	19×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
6	36
5	35
4	33
3	30
2	24
1	14
0	7

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.5b

localize46.0ms

Local error

Found 1 expressions with local error:

5.0b	(- (exp x) (exp (- x)))

rewrite39.0ms

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:

37.0ms

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

series74.0ms

Counts

1 → 3

Calls

1 calls:

74.0ms

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

simplify6.5s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
4	4689
3	1172
2	418
1	170
0	73

prune207.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l` `fma-udef`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

1.0ms	(fma (pow x 5) 1/60 (* x (fma (* x x) 1/3 2)))
14.0ms	(* x (fma (* x x) 1/3 2))

series289.0ms

Counts

2 → 6

Calls

2 calls:

110.0ms	(fma (pow x 5) 1/60 (* x (fma (* x x) 1/3 2)))
180.0ms	(* x (fma (* x x) 1/3 2))

simplify2.8s

Counts

38 → 38

Iterations

Iter	Nodes
done	5002
3	1607
2	372
1	133
0	63

prune314.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (* (* x x) 1/3)) (* x 2))
0.0b	(fma (pow x 5) 1/60 (+ (* x (* (* x x) 1/3)) (* x 2)))
0.1b	(* x (* (* x x) 1/3))
0.2b	(* (* x x) 1/3)

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u`
2×	`*-commutative`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

91.0ms	(+ (* x (* (* x x) 1/3)) (* x 2))
1.0ms	(fma (pow x 5) 1/60 (+ (* x (* (* x x) 1/3)) (* x 2)))
99.0ms	(* x (* (* x x) 1/3))
38.0ms	(* (* x x) 1/3)

series422.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(+ (* x (* (* x x) 1/3)) (* x 2))
110.0ms	(fma (pow x 5) 1/60 (+ (* x (* (* x x) 1/3)) (* x 2)))
70.0ms	(* x (* (* x x) 1/3))
52.0ms	(* (* x x) 1/3)

simplify6.5s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4399
2	971
1	281
0	108

prune636.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))) (+ (exp x) (exp (- x))))
0.0b	(* (exp x) (exp x))
0.1b	(* (exp (- x)) (exp (- x)))
5.0b	(- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

94×	`exp-prod`
70×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
24×	`distribute-rgt-neg-in`
20×	`distribute-lft-neg-in`
19×	`pow-prod-down`
18×	`pow1`
17×	`pow-sqr` `pow-prod-up`
16×	`times-frac`
10×	`add-cbrt-cube`
8×	`neg-mul-1`
7×	`exp-neg`
6×	`add-exp-log` `neg-sub0` `exp-diff` `swap-sqr` `associate-r` `associate-l` `add-log-exp` `difference-of-squares`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`pow2` `flip3--` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `un-div-inv` `flip-+` `div-inv`

Counts

4 → 170

Calls

4 calls:

124.0ms	(/ (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))) (+ (exp x) (exp (- x))))
39.0ms	(* (exp x) (exp x))
104.0ms	(* (exp (- x)) (exp (- x)))
39.0ms	(- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x)))) (+ (exp x) (exp (- x))))
28.0ms	(* (exp x) (exp x))
33.0ms	(* (exp (- x)) (exp (- x)))
124.0ms	(- (* (exp x) (exp x)) (* (exp (- x)) (exp (- x))))

simplify4.4s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
2	1760
1	575
0	225

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	18
1	18
0	14

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.8s	3372×	body	1280	valid
1.0s	2423×	body	640	valid
603.0ms	8054×	body	80	valid
349.0ms	1246×	body	320	valid
211.0ms	685×	body	160	valid