Details

sample121.0ms

Algorithm

intervals

Results

28.0ms	192×	body	80	valid
26.0ms	30×	body	2560	valid
19.0ms	26×	body	1280	valid
13.0ms	99×	body	80	nan
7.0ms	12×	body	640	valid
5.0ms	5×	body	5120	valid
2.0ms	5×	body	320	valid
1.0ms	2×	body	160	valid

simplify89.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.3b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.6b	(- (* b b) (* (* 3 a) c))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

106.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
63.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
12.0ms	(- (* b b) (* (* 3 a) c))
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
124.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
78.0ms	(- (* b b) (* (* 3 a) c))
87.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.0s

Counts

88 → 88

Iterations

Iter	Nodes
3	4845
2	1248
1	393
0	157

prune907.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* 3 a))
0.3b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.6b	(- (* b b) (* (* 3 a) c))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt`
4×	`div-exp` `sqrt-prod` `insert-posit16`
3×	`times-frac` `flip3--` `prod-exp` `flip--` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp` `pow-flip` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `cbrt-unprod` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 74

Calls

4 calls:

9.0ms	(/ 1 (* 3 a))
33.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
8.0ms	(- (* b b) (* (* 3 a) c))
11.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (* 3 a))
110.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
77.0ms	(- (* b b) (* (* 3 a) c))
108.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.0s

Counts

86 → 86

Iterations

Iter	Nodes
3	3439
2	964
1	324
0	140

prune807.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b	(/ 1/3 a)
0.6b	(- (* b b) (* (* 3 a) c))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-/r` `flip3--` `flip--` `associate-/l`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv` `distribute-lft-out--`

Counts

4 → 73

Calls

4 calls:

284.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
4.0ms	(/ 1/3 a)
7.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.0ms	(/ 1/3 a)
66.0ms	(- (* b b) (* (* 3 a) c))
77.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.4s

Counts

85 → 85

Iterations

Iter	Nodes
3	2864
2	872
1	298
0	141

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3 a) c))
9.5b	(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`
1×	`difference-of-squares`

Counts

4 → 59

Calls

4 calls:

15.0ms	(- (* b b) (* (* 3 a) c))
73.0ms	(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
13.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b b) (* (* 3 a) c))
84.0ms	(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
82.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.2s

Counts

71 → 71

Iterations

Iter	Nodes
3	2753
2	743
1	230
0	96

prune815.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.9b

regimes457.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.5b against oracle of 5.8b and baseline of 33.3b

bsearch176.0ms

Steps

Iters	Range		Point
6	3.7222086374392734e-21	4.963951531010332e-20	3.821014310434392e-21
10	-3.568388406125044e+108	-3.585760457965514e+97	-4.525652579795996e+106

simplify8.0ms

Iterations

Iter	Nodes
2	34
1	34
0	28

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.1s	5858×	body	80	valid
716.0ms	1029×	body	2560	valid
487.0ms	889×	body	1280	valid
329.0ms	2861×	body	80	nan
221.0ms	469×	body	640	valid
107.0ms	107×	body	5120	valid
76.0ms	201×	body	320	valid
26.0ms	139×	body	160	valid