Details

sample57.0ms

Algorithm

intervals

Results

11.0ms	188×	body	80	valid
10.0ms	27×	body	2560	valid
6.0ms	21×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	13×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma p (* 4.0 p) (* x x))
0.0b	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
14.0b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `flip-+` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma p (* 4.0 p) (* x x))
14.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
25.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
3.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma p (* 4.0 p) (* x x))
102.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
142.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
100.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify3.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
4	4938
3	1451
2	518
1	222
0	116

prune459.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 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)))))))
14.0b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`log-pow`
4×	`expm1-log1p-u` `log-prod` `exp-prod` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `rem-log-exp` `exp-sum` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

5.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
46.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))))
2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
85.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
87.0ms	(log (exp (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))))
70.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify1.9s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
4	4270
3	1430
2	566
1	244
0	130

prune566.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (fma p (* 4.0 p) (* x x))))
0.2b	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
2.6b	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
14.0b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
26×	`sqrt-prod`
22×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u`
3×	`fma-def` `associate-l` `pow-flip` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `flip3-+` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 127

Calls

4 calls:

6.0ms	(/ 1 (sqrt (fma p (* 4.0 p) (* x x))))
21.0ms	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
5.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ 1 (sqrt (fma p (* 4.0 p) (* x x))))
64.0ms	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
85.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
66.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify1.9s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	2119
2	920
1	325
0	147

prune562.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
8.6b	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))))
14.0b	(sqrt (fma p (* 4.0 p) (* x x)))
14.0b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

37×	`sqrt-prod`
25×	`associate-r`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
11×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `+-commutative` `sum-log` `flip3-+` `associate-l` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

55.0ms	(* (* x (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
5.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))))
1.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
1.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* x (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
84.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))) (sqrt (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))))
66.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
71.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify1.7s

Counts

103 → 103

Iterations

Iter	Nodes
done	5003
3	2516
2	928
1	337
0	142

prune498.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.9b

regimes157.0ms

Accuracy

0% (0.3b remaining)

Error of 13.9b against oracle of 13.6b and baseline of 13.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

590.0ms	5946×	body	80	valid
349.0ms	756×	body	2560	valid
199.0ms	8000×	pre	80	true
178.0ms	651×	body	1280	valid
59.0ms	322×	body	640	valid
27.0ms	182×	body	320	valid
22.0ms	61×	body	5120	valid
9.0ms	82×	body	160	valid