Details

sample68.0ms

Algorithm

intervals

Results

13.0ms	256×	pre	80	true
12.0ms	197×	body	80	valid
8.0ms	23×	body	1280	valid
8.0ms	19×	body	2560	valid
2.0ms	7×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify120.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
0.4b	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
12.1b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`flip3-+` `pow1/2` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `pow-prod-down` `distribute-lft-out`

Counts

3 → 50

Calls

3 calls:

23.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
44.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
5.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series689.0ms

Counts

3 → 9

Calls

3 calls:

446.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
131.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
112.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify3.6s

Counts

59 → 59

Iterations

Iter	Nodes
done	5003
4	2111
3	812
2	344
1	152
0	82

prune599.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x))))))
0.4b	(+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x)))))
0.4b	(log (exp (+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x)))))))
12.1b	(sqrt (fma (* p 4.0) p (* x x)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
8×	`exp-prod`
6×	`pow1`
5×	`log-pow`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `distribute-lft-out`
2×	`sum-log` `exp-sum` `rem-exp-log`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `flip-+`

Counts

4 → 71

Calls

4 calls:

71.0ms	(exp (+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x))))))
19.0ms	(+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x)))))
74.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x)))))))
3.0ms	(sqrt (fma (* p 4.0) p (* x x)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(exp (+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x))))))
109.0ms	(+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x)))))
109.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma (* p 4.0) p (* x x)))))))
82.0ms	(sqrt (fma (* p 4.0) p (* x x)))

simplify4.9s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
5	4554
4	1879
3	930
2	422
1	175
0	91

prune831.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.6b

localize130.0ms

Local error

Found 4 expressions with local error:

2.1b	(/ (* x (/ (* x x) (sqrt (fma (* p 4.0) p (* x x))))) (fma (* p 4.0) p (* x x)))
12.1b	(sqrt (fma (* p 4.0) p (* x x)))
12.1b	(sqrt (fma (* p 4.0) p (* x x)))
12.1b	(sqrt (fma (* p 4.0) p (* x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

28.0ms	(/ (* x (/ (* x x) (sqrt (fma (* p 4.0) p (* x x))))) (fma (* p 4.0) p (* x x)))
3.0ms	(sqrt (fma (* p 4.0) p (* x x)))
3.0ms	(sqrt (fma (* p 4.0) p (* x x)))
3.0ms	(sqrt (fma (* p 4.0) p (* x x)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (* x (/ (* x x) (sqrt (fma (* p 4.0) p (* x x))))) (fma (* p 4.0) p (* x x)))
84.0ms	(sqrt (fma (* p 4.0) p (* x x)))
85.0ms	(sqrt (fma (* p 4.0) p (* x x)))
81.0ms	(sqrt (fma (* p 4.0) p (* x x)))

simplify1.8s

Counts

89 → 89

Iterations

Iter	Nodes
done	5002
2	1104
1	263
0	92

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (fma p (* 4.0 p) (* x x)))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))
6.0b	(+ 1.0 (/ x (* (sqrt (sqrt (fma p (* 4.0 p) (* x x)))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))))
12.1b	(sqrt (fma p (* 4.0 p) (* x x)))
12.1b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`rem-sqrt-square`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 128

Calls

4 calls:

28.0ms	(* (sqrt (sqrt (fma p (* 4.0 p) (* x x)))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))
25.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (fma p (* 4.0 p) (* x x)))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))))
3.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
3.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sqrt (sqrt (fma p (* 4.0 p) (* x x)))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))
106.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (fma p (* 4.0 p) (* x x)))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))))
81.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
81.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify2.8s

Counts

140 → 140

Iterations

Iter	Nodes
done	5021
3	1702
2	541
1	245
0	119

prune933.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.5b

regimes436.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	27
1	27
0	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

411.0ms	599×	body	1280	valid
377.0ms	744×	body	2560	valid
334.0ms	6027×	body	80	valid
205.0ms	8000×	pre	80	true
59.0ms	324×	body	640	valid
25.0ms	172×	body	320	valid
23.0ms	58×	body	5120	valid
7.0ms	76×	body	160	valid