Details

sample372.0ms

Algorithm

intervals

Results

53.0ms	35×	body	2560	valid
50.0ms	196×	body	80	valid
47.0ms	31×	body	1280	valid
40.0ms	89×	body	80	nan
33.0ms	2×	body	320	valid
4.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	3×	body	160	valid

simplify207.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize83.0ms

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)))

rewrite319.0ms

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:

193.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
62.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
191.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2152
1	583
0	244

prune747.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize41.0ms

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)))

rewrite117.0ms

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:

56.0ms	(/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) (- a))
13.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) (- a))
49.0ms	(- (* b_2 b_2) (* a c))
126.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	1703
1	453
0	193

prune729.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize46.0ms

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)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 257

Calls

4 calls:

87.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
56.0ms	(- (* b_2 b_2) (* a c))
130.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

269 → 269

Iterations

Iter	Nodes
done	5000
2	4146
1	850
0	351

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize47.0ms

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)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
34×	`associate-r`
32×	`*-un-lft-identity` `times-frac`
27×	`add-cube-cbrt`
13×	`add-exp-log`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u`
3×	`neg-mul-1` `fma-def` `flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod` `flip--` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `1-exp` `prod-diff` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 114

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
131.0ms	(* (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 (- a)))
25.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b_2 b_2) (* a c))
116.0ms	(* (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 (- a)))
99.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify7.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	4172
1	595
0	220

prune882.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes392.0ms

Accuracy

87% (3.7b remaining)

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

bsearch272.0ms

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

simplify13.0ms

Iterations

Iter	Nodes
done	36
2	36
1	35
0	30

end0.0ms

sample2.9s

Algorithm

intervals

Results

869.0ms	1136×	body	2560	valid
621.0ms	5799×	body	80	valid
293.0ms	868×	body	1280	valid
249.0ms	2815×	body	80	nan
109.0ms	446×	body	640	valid
88.0ms	109×	body	5120	valid
42.0ms	238×	body	320	valid
13.0ms	102×	body	160	valid