Details

sample138.0ms

Algorithm

intervals

Results

36.0ms	198×	body	80	valid
33.0ms	256×	pre	80	true
22.0ms	22×	body	2560	valid
15.0ms	16×	body	1280	valid
6.0ms	9×	body	640	valid
4.0ms	8×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	2×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize434.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma p (* 4 p) (* x x))
0.0b	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.4b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
18.9b	(sqrt (fma p (* 4 p) (* x x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

0.0ms	(fma p (* 4 p) (* x x))
5.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma p (* 4 p) (* x x))
79.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
115.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
82.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
4	3315
3	885
2	304
1	166
0	108

prune989.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize36.0ms

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)))))
1.8b	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
18.9b	(sqrt (fma p (* 4 p) (* x x)))

rewrite31.0ms

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:

2.0ms	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
24.0ms	(* 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)
2.0ms	(sqrt (fma p (* 4 p) (* x x)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
80.0ms	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
120.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
92.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify5.7s

Counts

105 → 105

Iterations

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

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* p 4) p (* x x))
0.0b	(/ x (sqrt (fma (* p 4) p (* x x))))
0.4b	(fma 0.5 (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5)
18.9b	(sqrt (fma (* p 4) p (* x x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

0.0ms	(fma (* p 4) p (* x x))
9.0ms	(/ x (sqrt (fma (* p 4) p (* x x))))
0.0ms	(fma 0.5 (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5)
2.0ms	(sqrt (fma (* p 4) p (* x x)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma (* p 4) p (* x x))
75.0ms	(/ x (sqrt (fma (* p 4) p (* x x))))
100.0ms	(fma 0.5 (/ x (sqrt (fma (* p 4) p (* x x)))) 0.5)
65.0ms	(sqrt (fma (* p 4) p (* x x)))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
4	3230
3	839
2	298
1	166
0	108

prune834.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.0b

localize71.0ms

Local error

Found 4 expressions with local error:

1.8b	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
18.9b	(sqrt (fma p (* 4 p) (* x x)))
18.9b	(sqrt (fma p (* 4 p) (* x x)))
18.9b	(sqrt (fma p (* 4 p) (* x x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
3.0ms	(sqrt (fma p (* 4 p) (* x x)))
2.0ms	(sqrt (fma p (* 4 p) (* x x)))
3.0ms	(sqrt (fma p (* 4 p) (* x x)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
57.0ms	(sqrt (fma p (* 4 p) (* x x)))
84.0ms	(sqrt (fma p (* 4 p) (* x x)))
87.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify3.9s

Counts

71 → 71

Iterations

Iter	Nodes
5	5522
4	1116
3	278
2	106
1	62
0	45

prune975.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.0b

regimes152.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	6007×	body	80	valid
615.0ms	757×	body	2560	valid
389.0ms	618×	body	1280	valid
283.0ms	8000×	pre	80	true
135.0ms	333×	body	640	valid
67.0ms	151×	body	320	valid
52.0ms	68×	body	5120	valid
14.0ms	66×	body	160	valid