Details

sample108.0ms

Algorithm

intervals

Results

32.0ms	76×	body	1280	valid
28.0ms	75×	body	10240	exit
14.0ms	50×	body	640	valid
5.0ms	91×	body	80	valid
5.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize47.0ms

Local error

Found 2 expressions with local error:

1.2b	(/ (exp x) (- (exp x) 1.0))
3.2b	(- (exp x) 1.0)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `insert-posit16` `log1p-expm1-u` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 69

Calls

2 calls:

78.0ms	(/ (exp x) (- (exp x) 1.0))
47.0ms	(- (exp x) 1.0)

series75.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (exp x) (- (exp x) 1.0))
19.0ms	(- (exp x) 1.0)

simplify4.3s

Counts

75 → 75

Iterations

Iter	Nodes
done	5050
3	2105
2	676
1	254
0	119

prune520.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize67.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma (* x x) (fma 1/6 x 1/2) x))
0.1b	(fma (* x x) (fma 1/6 x 1/2) x)
0.1b	(fma 1/6 x 1/2)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

Calls

3 calls:

33.0ms	(/ (exp x) (fma (* x x) (fma 1/6 x 1/2) x))
2.0ms	(fma (* x x) (fma 1/6 x 1/2) x)
2.0ms	(fma 1/6 x 1/2)

series142.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (exp x) (fma (* x x) (fma 1/6 x 1/2) x))
33.0ms	(fma (* x x) (fma 1/6 x 1/2) x)
56.0ms	(fma 1/6 x 1/2)

simplify8.4s

Counts

61 → 61

Iterations

Iter	Nodes
done	5157
3	2669
2	609
1	196
0	100

prune662.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 1 x) (fma x 1/12 1/2))
0.1b	(fma x 1/12 1/2)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

13×	`fma-def`
12×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
4×	`add-log-exp`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u` `div-inv` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `sum-log` `flip3-+` `flip-+`

Counts

2 → 41

Calls

2 calls:

37.0ms	(+ (/ 1 x) (fma x 1/12 1/2))
1.0ms	(fma x 1/12 1/2)

series71.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (/ 1 x) (fma x 1/12 1/2))
45.0ms	(fma x 1/12 1/2)

simplify8.9s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	4623
3	1286
2	349
1	107
0	45

prune445.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp x))
1.0b	(* (/ 1 (+ (sqrt (exp x)) (sqrt 1.0))) (/ (exp x) (- (sqrt (exp x)) (sqrt 1.0))))
1.0b	(/ (exp x) (- (sqrt (exp x)) (sqrt 1.0)))
3.2b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite494.0ms

Algorithm

rewrite-expression-head

Rules

150×	`add-sqr-sqrt`
114×	`*-un-lft-identity`
96×	`sqrt-prod`
76×	`times-frac`
68×	`add-cube-cbrt`
36×	`prod-diff`
33×	`associate-r`
32×	`difference-of-squares`
23×	`add-exp-log`
21×	`associate-l`
18×	`add-cbrt-cube`
16×	`distribute-lft-out--`
9×	`associate-/r*` `div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`fma-neg` `associate-/r/` `distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-pow1` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `flip3--` `div-inv` `flip--` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`frac-times` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

4 → 225

Calls

4 calls:

8.0ms	(sqrt (exp x))
307.0ms	(* (/ 1 (+ (sqrt (exp x)) (sqrt 1.0))) (/ (exp x) (- (sqrt (exp x)) (sqrt 1.0))))
94.0ms	(/ (exp x) (- (sqrt (exp x)) (sqrt 1.0)))
63.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series783.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (exp x))
466.0ms	(* (/ 1 (+ (sqrt (exp x)) (sqrt 1.0))) (/ (exp x) (- (sqrt (exp x)) (sqrt 1.0))))
232.0ms	(/ (exp x) (- (sqrt (exp x)) (sqrt 1.0)))
66.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify5.5s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	2594
1	815
0	303

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

regimes365.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 22.1b

bsearch40.0ms

Steps

Iters	Range		Point
8	-0.28008678268591264	-0.00018185218373056224	-0.043762652068368615

simplify11.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	2564×	body	10240	exit
901.0ms	1647×	body	640	valid
830.0ms	2148×	body	1280	valid
270.0ms	2958×	body	80	valid
187.0ms	828×	body	320	valid
51.0ms	420×	body	160	valid