Details

sample354.0ms

Algorithm

intervals

Results

104.0ms	123×	body	320	valid
36.0ms	234×	body	80	nan
35.0ms	490×	pre	80	true
28.0ms	82×	body	160	valid
12.0ms	20×	body	640	valid
5.0ms	31×	body	80	valid

simplify146.0ms

Counts

1 → 1

Iterations

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

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma b b (* (* a -4) c))
0.0b	(sqrt (fma b b (* (* a -4) c)))
0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
25.1b	(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite30.0ms

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:

0.0ms	(fma b b (* (* a -4) c))
1.0ms	(sqrt (fma b b (* (* a -4) c)))
17.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
9.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)

series524.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma b b (* (* a -4) c))
121.0ms	(sqrt (fma b b (* (* a -4) c)))
187.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
147.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)

simplify1.4s

Counts

126 → 126

Iterations

Iter	Nodes
3	2589
2	949
1	405
0	180

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.3b

localize17.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
1	0
0	0

prune59.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.3b

localize29.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(/ (* -2 (/ (* a c) b)) a)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
8×	`cbrt-undiv` `div-exp`
6×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `add-cube-cbrt`
5×	`prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 53

Calls

2 calls:

18.0ms	(/ (* a c) b)
31.0ms	(/ (* -2 (/ (* a c) b)) a)

series61.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ (* a c) b)
28.0ms	(/ (* -2 (/ (* a c) b)) a)

simplify2.4s

Counts

59 → 59

Iterations

Iter	Nodes
3	6399
2	1058
1	267
0	103

prune566.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 2.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ -2 b) (/ c 1))
0.4b	(* (* (/ -2 b) (/ c 1)) (* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1))))
0.5b	(* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1)))
0.7b	(cbrt (* (* (/ -2 b) (/ c 1)) (* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1)))))

rewrite582.0ms

Algorithm

rewrite-expression-head

Rules

2944×	`add-exp-log`
1720×	`prod-exp`
1141×	`div-exp`
1139×	`add-cbrt-cube`
628×	`cbrt-unprod`
348×	`cbrt-undiv`
326×	`1-exp`
276×	`frac-times`
173×	`pow1`
162×	`associate-*r/`
138×	`associate-*l/`
78×	`pow-prod-down`
63×	`cbrt-div`
35×	`add-sqr-sqrt`
34×	`pow-prod-up`
25×	`times-frac`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`associate-r` `associate-l`
12×	`pow-sqr`
6×	`pow-plus` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `*-commutative`
2×	`cube-unmult` `div-inv`
1×	`cbrt-prod` `pow1/3` `swap-sqr` `rem-cbrt-cube`

Counts

4 → 840

Calls

4 calls:

25.0ms	(* (/ -2 b) (/ c 1))
231.0ms	(* (* (/ -2 b) (/ c 1)) (* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1))))
69.0ms	(* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1)))
205.0ms	(cbrt (* (* (/ -2 b) (/ c 1)) (* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1)))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ -2 b) (/ c 1))
111.0ms	(* (* (/ -2 b) (/ c 1)) (* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1))))
77.0ms	(* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1)))
77.0ms	(cbrt (* (* (/ -2 b) (/ c 1)) (* (* (/ -2 b) (/ c 1)) (* (/ -2 b) (/ c 1)))))

simplify3.9s

Counts

852 → 852

Iterations

Iter	Nodes
2	5230
1	1894
0	930

prune7.1s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 2.3b

regimes446.0ms

Accuracy

0% (3.6b remaining)

Error of 6.3b against oracle of 2.7b and baseline of 6.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	8
1	8
0	7

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.3s	3644×	body	320	valid
1.2s	8149×	body	80	nan
1.1s	16149×	pre	80	true
996.0ms	2909×	body	160	valid
331.0ms	524×	body	640	valid
138.0ms	923×	body	80	valid