Details

sample63.0ms

Algorithm

intervals

Results

12.0ms	189×	body	80	valid
11.0ms	27×	body	2560	valid
8.0ms	24×	body	1280	valid
6.0ms	256×	pre	80	true
2.0ms	10×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify78.0ms

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
0.0b	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
1.0b	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
16.6b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

37.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
10.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
24.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series751.0ms

Counts

4 → 12

Calls

4 calls:

408.0ms	(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
103.0ms	(/ x (sqrt (fma p (* 4.0 p) (* x x))))
136.0ms	(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
104.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify3.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
4	4580
3	1393
2	523
1	230
0	128

prune633.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.1b

localize64.0ms

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)))))
3.6b	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
16.6b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite51.0ms

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))))
29.0ms	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
9.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
3.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1 (sqrt (fma p (* 4.0 p) (* x x))))
83.0ms	(* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x)))))
106.0ms	(+ 1.0 (* x (/ 1 (sqrt (fma p (* 4.0 p) (* x x))))))
96.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify2.8s

Counts

139 → 139

Iterations

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

prune741.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 (sqrt (sqrt (fma p (* 4.0 p) (* x x))))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))
8.5b	(+ 1.0 (* x (/ (/ 1 (sqrt (sqrt (fma p (* 4.0 p) (* x x))))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))))
16.6b	(sqrt (fma p (* 4.0 p) (* x x)))
16.6b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

564×	`sqrt-prod`
549×	`times-frac`
295×	`add-sqr-sqrt`
293×	`*-un-lft-identity` `add-cube-cbrt`
31×	`associate-/l*`
18×	`sqrt-pow1`
17×	`pow1`
13×	`add-exp-log`
11×	`div-inv`
10×	`pow1/2` `pow-div`
9×	`associate-/r*` `add-cbrt-cube` `pow-flip`
6×	`div-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def`
2×	`rem-sqrt-square`
1×	`+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `flip3-+` `1-exp` `flip-+` `inv-pow` `associate-/l/`

Counts

4 → 394

Calls

4 calls:

30.0ms	(/ (/ 1 (sqrt (sqrt (fma p (* 4.0 p) (* x x))))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))
7.0ms	(+ 1.0 (* x (/ (/ 1 (sqrt (sqrt (fma p (* 4.0 p) (* x x))))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))))
2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (/ 1 (sqrt (sqrt (fma p (* 4.0 p) (* x x))))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))
87.0ms	(+ 1.0 (* x (/ (/ 1 (sqrt (sqrt (fma p (* 4.0 p) (* x x))))) (sqrt (sqrt (fma p (* 4.0 p) (* x x)))))))
85.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
76.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify2.0s

Counts

406 → 406

Iterations

Iter	Nodes
done	5000
2	1648
1	934
0	417

prune2.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 14.1b

localize93.0ms

Local error

Found 4 expressions with local error:

16.6b	(sqrt (fma p (* 4.0 p) (* x x)))
16.6b	(sqrt (fma p (* 4.0 p) (* x x)))
16.6b	(sqrt (fma p (* 4.0 p) (* x x)))
16.6b	(sqrt (fma p (* 4.0 p) (* x x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
2.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
77.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
87.0ms	(sqrt (fma p (* 4.0 p) (* x x)))
89.0ms	(sqrt (fma p (* 4.0 p) (* x x)))

simplify3.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
9	1076
8	392
7	223
6	170
5	143
4	125
3	95
2	66
1	42
0	28

prune625.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 14.1b

regimes135.0ms

Accuracy

0% (0.4b remaining)

Error of 13.3b against oracle of 12.9b and baseline of 13.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample2.0s

Algorithm

intervals

Results

859.0ms	6045×	body	80	valid
374.0ms	755×	body	2560	valid
253.0ms	652×	body	1280	valid
198.0ms	8000×	pre	80	true
79.0ms	297×	body	640	valid
25.0ms	134×	body	320	valid
22.0ms	46×	body	5120	valid
9.0ms	71×	body	160	valid