Details

sample130.0ms

Algorithm

intervals

Results

48.0ms	193×	body	80	valid
23.0ms	30×	body	2560	valid
15.0ms	26×	body	1280	valid
11.0ms	99×	body	80	nan
6.0ms	12×	body	640	valid
4.0ms	5×	body	5120	valid
2.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify152.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.2b	(- (sqrt (fma b b (* (* a -4) c))) b)
0.8b	(fma b b (* (* a -4) c))
24.5b	(sqrt (fma b b (* (* a -4) c)))

rewrite51.0ms

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:

34.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
11.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms	(fma b b (* (* a -4) c))
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
153.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
64.0ms	(fma b b (* (* a -4) c))
129.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
3	2626
2	950
1	405
0	180

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma b b (* (* a -4) c))
0.8b	(fma b b (* (* a -4) c))
24.5b	(sqrt (fma b b (* (* a -4) c)))
24.5b	(sqrt (fma b b (* (* a -4) c)))

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

series419.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(fma b b (* (* a -4) c))
71.0ms	(fma b b (* (* a -4) c))
123.0ms	(sqrt (fma b b (* (* a -4) c)))
131.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.0s

Counts

66 → 66

Iterations

Iter	Nodes
4	2419
3	634
2	216
1	92
0	49

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (fma b b (* (* a -4) c))) a)
0.8b	(fma b b (* (* a -4) c))
6.7b	(- (/ (sqrt (fma b b (* (* a -4) c))) a) (/ b a))
24.5b	(sqrt (fma b b (* (* a -4) c)))

rewrite68.0ms

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:

9.0ms	(/ (sqrt (fma b b (* (* a -4) c))) a)
0.0ms	(fma b b (* (* a -4) c))
38.0ms	(- (/ (sqrt (fma b b (* (* a -4) c))) a) (/ b a))
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (sqrt (fma b b (* (* a -4) c))) a)
71.0ms	(fma b b (* (* a -4) c))
175.0ms	(- (/ (sqrt (fma b b (* (* a -4) c))) a) (/ b a))
120.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.1s

Counts

417 → 417

Iterations

Iter	Nodes
2	2333
1	1062
0	479

prune5.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

localize91.0ms

Local error

Found 4 expressions with local error:

24.5b	(sqrt (fma b b (* (* a -4) c)))
25.3b	(cbrt (fma b b (* (* a -4) c)))
25.3b	(cbrt (fma b b (* (* a -4) c)))
25.3b	(cbrt (fma b b (* (* a -4) c)))

rewrite8.0ms

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

series493.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt (fma b b (* (* a -4) c)))
105.0ms	(cbrt (fma b b (* (* a -4) c)))
122.0ms	(cbrt (fma b b (* (* a -4) c)))
163.0ms	(cbrt (fma b b (* (* a -4) c)))

simplify3.2s

Counts

70 → 70

Iterations

Iter	Nodes
5	4129
4	1643
3	759
2	324
1	147
0	72

prune1.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.9b

regimes418.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.5b

bsearch237.0ms

Steps

Iters	Range		Point
6	3.7222086374392734e-21	4.963951531010332e-20	3.821014310434392e-21
10	-3.568388406125044e+108	-3.585760457965514e+97	-5.571206846913461e+106

simplify9.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.6s	1029×	body	2560	valid
1.4s	5860×	body	80	valid
683.0ms	889×	body	1280	valid
410.0ms	2862×	body	80	nan
324.0ms	469×	body	640	valid
131.0ms	107×	body	5120	valid
78.0ms	199×	body	320	valid
39.0ms	141×	body	160	valid