Details

sample95.0ms

Algorithm

intervals

Results

30.0ms	34×	body	2560	valid
20.0ms	198×	body	80	valid
15.0ms	29×	body	1280	valid
9.0ms	91×	body	80	nan
3.0ms	8×	body	640	valid
2.0ms	7×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	6×	body	160	valid

simplify145.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.2b	(- (* b b) (* (* c a) 4))
1.3b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
27.8b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

84.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
12.0ms	(- (* b b) (* (* c a) 4))
54.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
68.0ms	(- (* b b) (* (* c a) 4))
99.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
78.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
3	3565
2	1088
1	398
0	161

prune868.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
1.2b	(- (* b b) (* (* c a) 4))
1.3b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
27.8b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

113.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
15.0ms	(- (* b b) (* (* c a) 4))
43.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
16.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
66.0ms	(- (* b b) (* (* c a) 4))
109.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
76.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify3.3s

Counts

101 → 101

Iterations

Iter	Nodes
3	5062
2	1496
1	461
0	181

prune986.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
1.2b	(- (* b b) (* (* c a) 4))
1.3b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
27.8b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-l` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `prod-exp` `insert-posit16` `difference-of-squares`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `diff-log` `div-exp` `associate-*r/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 92

Calls

4 calls:

139.0ms	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
9.0ms	(- (* b b) (* (* c a) 4))
37.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (/ 1 a) (- (sqrt (- (* b b) (* (* c a) 4))) b))
54.0ms	(- (* b b) (* (* c a) 4))
91.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
105.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.3s

Counts

104 → 104

Iterations

Iter	Nodes
3	3875
2	1288
1	443
0	169

prune935.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
1.2b	(- (* b b) (* (* c a) 4))
1.3b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
27.8b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 166

Calls

4 calls:

56.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
14.0ms	(- (* b b) (* (* c a) 4))
46.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
66.0ms	(- (* b b) (* (* c a) 4))
100.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
112.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify5.7s

Counts

178 → 178

Iterations

Iter	Nodes
3	5448
2	1712
1	646
0	265

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.7b

regimes839.0ms

Accuracy

82.3% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.5b

bsearch223.0ms

Steps

Iters	Range		Point
8	2.764110880089542e-64	2.3245141193625934e-60	2.0617732603635578e-61
9	-229886301330938.94	-710549284.1101115	-227369802444031.66

simplify11.0ms

Iterations

Iter	Nodes
4	48
3	48
2	44
1	40
0	31

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.0s	5886×	body	80	valid
989.0ms	1054×	body	2560	valid
846.0ms	908×	body	1280	valid
545.0ms	2993×	body	80	nan
481.0ms	232×	body	320	valid
324.0ms	446×	body	640	valid
145.0ms	110×	body	5120	valid
31.0ms	113×	body	160	valid