Details

sample133.0ms

Algorithm

intervals

Results

37.0ms	29×	body	1280	valid
28.0ms	198×	body	80	valid
14.0ms	17×	body	2560	valid
11.0ms	82×	body	80	nan
8.0ms	13×	body	640	valid
4.0ms	10×	body	320	valid
4.0ms	4×	body	5120	valid
3.0ms	10×	body	160	valid

simplify108.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	95
7	95
6	94
5	92
4	84
3	67
2	43
1	24
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
1.2b	(- (* b b) (* (* 4 a) c))
2.7b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite139.0ms

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:

77.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
7.0ms	(- (* b b) (* (* 4 a) c))
42.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
62.0ms	(- (* b b) (* (* 4 a) c))
134.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
90.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts

100 → 100

Iterations

Iter	Nodes
3	3741
2	1127
1	394
0	161

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
1.2b	(- (* b b) (* (* 4 a) c))
2.7b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite139.0ms

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:

66.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
16.0ms	(- (* b b) (* (* 4 a) c))
42.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
53.0ms	(- (* b b) (* (* 4 a) c))
115.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
115.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.6s

Counts

178 → 178

Iterations

Iter	Nodes
3	6120
2	1836
1	644
0	265

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (+ (* (* -4 a) c) (* b b))) b))
1.2b	(+ (* (* -4 a) c) (* b b))
2.7b	(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
22.2b	(sqrt (+ (* (* -4 a) c) (* b b)))

rewrite324.0ms

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×	`sqrt-prod`
4×	`prod-exp` `insert-posit16` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `sqrt-div` `div-exp` `associate-*r/` `cbrt-unprod` `flip-+` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

201.0ms	(* (/ 1 a) (- (sqrt (+ (* (* -4 a) c) (* b b))) b))
14.0ms	(+ (* (* -4 a) c) (* b b))
83.0ms	(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
23.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (/ 1 a) (- (sqrt (+ (* (* -4 a) c) (* b b))) b))
77.0ms	(+ (* (* -4 a) c) (* b b))
112.0ms	(- (sqrt (+ (* (* -4 a) c) (* b b))) b)
111.0ms	(sqrt (+ (* (* -4 a) c) (* b b)))

simplify1.6s

Counts

103 → 103

Iterations

Iter	Nodes
3	3868
2	1182
1	414
0	157

prune917.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
1.2b	(- (* b b) (* (* 4 a) c))
7.1b	(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

13.0ms	(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
7.0ms	(- (* b b) (* (* 4 a) c))
45.0ms	(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
64.0ms	(- (* b b) (* (* 4 a) c))
131.0ms	(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
87.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts

109 → 109

Iterations

Iter	Nodes
3	3416
2	1130
1	410
0	179

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

regimes315.0ms

Accuracy

89.6% (2.9b remaining)

Error of 8.7b against oracle of 5.8b and baseline of 33.8b

bsearch357.0ms

Steps

Iters	Range	Point
6	1.890398075878753e+149	8.723340275486535e+149	1.9081232567651569e+149
7	2.2186536445016797e-183	5.112611773443175e-182	4.634052056998666e-182
10	-4.8388360275630777e+135	-9.113678877832951e+119	-1.3725796156555912e+127

Iters

Range

Point

1.890398075878753e+149

8.723340275486535e+149

1.9081232567651569e+149

2.2186536445016797e-183

5.112611773443175e-182

4.634052056998666e-182

-4.8388360275630777e+135

-9.113678877832951e+119

-1.3725796156555912e+127

simplify17.0ms

Iterations

Iter	Nodes
2	50
1	50
0	41

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.0s	5930×	body	80	valid
1.0s	1043×	body	2560	valid
873.0ms	2880×	body	80	nan
786.0ms	886×	body	1280	valid
284.0ms	495×	body	640	valid
118.0ms	121×	body	5120	valid
111.0ms	202×	body	320	valid
31.0ms	116×	body	160	valid