Details

sample103.0ms

Algorithm

intervals

Results

35.0ms	36×	body	2560	valid
21.0ms	187×	body	80	valid
13.0ms	25×	body	1280	valid
9.0ms	86×	body	80	nan
8.0ms	17×	body	640	valid
3.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify110.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.8b	(fma (* a c) -4 (* b b))
0.9b	(- (sqrt (fma (* a c) -4 (* b b))) b)
23.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

40.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
15.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
74.0ms	(fma (* a c) -4 (* b b))
90.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
441.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify767.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	2003
2	718
1	319
0	156

prune714.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (fma (* a c) -4 (* b b))) a)
0.8b	(fma (* a c) -4 (* b b))
5.1b	(- (/ (sqrt (fma (* a c) -4 (* b b))) a) (/ b a))
23.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

481×	`times-frac`
378×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
358×	`add-cube-cbrt`
286×	`prod-diff`
143×	`sqrt-prod`
39×	`div-inv`
22×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-/r*`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `distribute-rgt-out--` `pow1/2` `diff-log` `div-exp` `frac-sub` `fma-udef` `flip--` `sub-div`

Counts

4 → 405

Calls

4 calls:

5.0ms	(/ (sqrt (fma (* a c) -4 (* b b))) a)
0.0ms	(fma (* a c) -4 (* b b))
19.0ms	(- (/ (sqrt (fma (* a c) -4 (* b b))) a) (/ b a))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (sqrt (fma (* a c) -4 (* b b))) a)
77.0ms	(fma (* a c) -4 (* b b))
139.0ms	(- (/ (sqrt (fma (* a c) -4 (* b b))) a) (/ b a))
115.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.1s

Counts

417 → 417

Iterations

Iter	Nodes
2	2100
1	970
0	453

prune2.2s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 31.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma (* a c) -4 (* b b))
21.3b	(fma (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))) (- b))
23.5b	(sqrt (fma (* a c) -4 (* b b)))
23.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

0.0ms	(fma (* a c) -4 (* b b))
0.0ms	(fma (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))) (- b))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
3.0ms	(sqrt (fma (* a c) -4 (* b b)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma (* a c) -4 (* b b))
378.0ms	(fma (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))) (- b))
92.0ms	(sqrt (fma (* a c) -4 (* b b)))
119.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.5s

Counts

66 → 66

Iterations

Iter	Nodes
4	2905
3	826
2	291
1	133
0	77

prune589.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 31.1b

localize94.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (fma (* a c) -4 (* b b)))
24.2b	(cbrt (fma (* a c) -4 (* b b)))
24.2b	(cbrt (fma (* a c) -4 (* b b)))
24.2b	(cbrt (fma (* a c) -4 (* b b)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

2.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(cbrt (fma (* a c) -4 (* b b)))
1.0ms	(cbrt (fma (* a c) -4 (* b b)))
2.0ms	(cbrt (fma (* a c) -4 (* b b)))

series854.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (fma (* a c) -4 (* b b)))
254.0ms	(cbrt (fma (* a c) -4 (* b b)))
232.0ms	(cbrt (fma (* a c) -4 (* b b)))
282.0ms	(cbrt (fma (* a c) -4 (* b b)))

simplify3.2s

Counts

70 → 70

Iterations

Iter	Nodes
5	6298
4	1995
3	665
2	254
1	121
0	67

prune612.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 31.1b

regimes742.0ms

Accuracy

81.6% (1.1b remaining)

Error of 29.4b against oracle of 28.3b and baseline of 34.4b

bsearch186.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	1.0088751240251126e+68

simplify5.0ms

Iterations

Iter	Nodes
2	27
1	27
0	25

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	1026×	body	2560	valid
977.0ms	5891×	body	80	valid
632.0ms	881×	body	1280	valid
419.0ms	2954×	body	80	nan
280.0ms	464×	body	640	valid
119.0ms	237×	body	320	valid
100.0ms	96×	body	5120	valid
26.0ms	104×	body	160	valid