Details

sample76.0ms

Algorithm

intervals

Results

20.0ms	196×	body	80	valid
12.0ms	35×	body	2560	valid
8.0ms	31×	body	1280	valid
6.0ms	89×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 171

Calls

4 calls:

76.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (* b_2 b_2) (* a c))
49.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
61.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2152
1	583
0	244

prune843.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) (- a))
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
40×	`times-frac`
33×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`distribute-lft-out`
10×	`associate-/r*`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `div-inv`

Counts

4 → 120

Calls

4 calls:

64.0ms	(/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) (- a))
9.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) (- a))
52.0ms	(- (* b_2 b_2) (* a c))
127.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	1703
1	453
0	193

prune824.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- a) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

298×	`times-frac`
227×	`*-un-lft-identity`
146×	`add-sqr-sqrt`
145×	`add-cube-cbrt`
48×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
46×	`associate-/r*`
41×	`distribute-lft-out`
16×	`neg-mul-1`
15×	`add-exp-log`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `sqrt-prod` `associate-/l*`
2×	`rec-exp` `flip3--` `sqrt-div` `1-exp` `flip--`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-flip` `inv-pow`

Counts

4 → 260

Calls

4 calls:

40.0ms	(/ 1 (/ (- a) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
6.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1 (/ (- a) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
44.0ms	(- (* b_2 b_2) (* a c))
115.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

272 → 272

Iterations

Iter	Nodes
done	5000
1	1013
0	375

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
41.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b_2 b_2) (* a c))
112.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
80.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	3750
1	653
0	263

prune803.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes344.0ms

Accuracy

87% (3.7b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 33.8b

bsearch176.0ms

Steps

Iters	Range	Point
10	4.0721326822252617e+40	3.6590220876252264e+50	3.628799960716312e+50
9	-8.630995884000565e-306	7.211886341925621e-305	-1.3410901614909383e-308
6	-1.278587798556269e+59	-1.7736353873113924e+58	-1.9700105655521088e+58

Iters

Range

Point

4.0721326822252617e+40

3.6590220876252264e+50

3.628799960716312e+50

-8.630995884000565e-306

7.211886341925621e-305

-1.3410901614909383e-308

-1.278587798556269e+59

-1.7736353873113924e+58

-1.9700105655521088e+58

simplify6.0ms

Iterations

Iter	Nodes
done	36
2	36
1	35
0	30

end0.0ms

sample2.5s

Algorithm

intervals

Results

509.0ms	446×	body	640	valid
490.0ms	1136×	body	2560	valid
412.0ms	5799×	body	80	valid
288.0ms	868×	body	1280	valid
176.0ms	2815×	body	80	nan
66.0ms	238×	body	320	valid
40.0ms	109×	body	5120	valid
10.0ms	102×	body	160	valid