Details

sample124.0ms

Algorithm

intervals

Results

27.0ms	182×	body	80	valid
25.0ms	27×	body	2560	valid
18.0ms	11×	body	640	valid
17.0ms	24×	body	1280	valid
12.0ms	256×	pre	80	true
3.0ms	6×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	5×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	48
4	48
3	46
2	40
1	28
0	14

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0b	(/ x (sqrt (fma p (* 4 p) (* x x))))
1.6b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
12.4b	(sqrt (fma p (* 4 p) (* x x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 85

Calls

4 calls:

2.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
10.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
2.0ms	(sqrt (fma p (* 4 p) (* x x)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
88.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
95.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
64.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify895.0ms

Counts

97 → 97

Iterations

Iter	Nodes
4	2335
3	722
2	288
1	161
0	110

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
0.8b	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
1.6b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
12.4b	(sqrt (fma p (* 4 p) (* x x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`log-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum` `sqrt-prod`
2×	`log-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `fma-udef` `rem-exp-log`

Counts

4 → 60

Calls

4 calls:

3.0ms	(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
1.0ms	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(exp (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
236.0ms	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
127.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
61.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify3.1s

Counts

72 → 72

Iterations

Iter	Nodes
5	4189
4	1160
3	390
2	196
1	125
0	86

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow E (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
0.8b	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
1.6b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
12.4b	(sqrt (fma p (* 4 p) (* x x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`log-prod` `add-exp-log`
4×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-up` `unpow-prod-down` `sqrt-prod`
2×	`pow-exp` `log-pow`
1×	`pow-to-exp` `rem-sqrt-square` `e-exp-1` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `fma-udef` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

5.0ms	(pow E (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
2.0ms	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series652.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(pow E (log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
195.0ms	(log (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
102.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
79.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify1.3s

Counts

79 → 79

Iterations

Iter	Nodes
4	2894
3	917
2	359
1	182
0	101

prune994.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 7.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
0.2b	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
4.7b	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
12.4b	(sqrt (fma p (* 4 p) (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

1.0ms	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
17.0ms	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
0.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
64.0ms	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
102.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
53.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify4.1s

Counts

105 → 105

Iterations

Iter	Nodes
4	3453
3	1329
2	547
1	264
0	132

prune849.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.5b

regimes64.0ms

Accuracy

-19.3% (9.3b remaining)

Error of 14.7b against oracle of 5.4b and baseline of 13.2b

bsearch73.0ms

Steps

Iters	Range		Point
6	-1.0697684771676703e+19	-1.5506507125207496e+18	-1.0089186447096822e+19

simplify5.0ms

Iterations

Iter	Nodes
2	27
1	27
0	24

end0.0ms

sample2.5s

Algorithm

intervals

Results

646.0ms	6044×	body	80	valid
464.0ms	631×	body	1280	valid
453.0ms	730×	body	2560	valid
417.0ms	309×	body	640	valid
285.0ms	8000×	pre	80	true
42.0ms	59×	body	5120	valid
37.0ms	138×	body	320	valid
16.0ms	89×	body	160	valid