Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
8.0ms	194×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	76×	body	80	nan
1.0ms	10×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(* (* 4.0 a) c)
2.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(* (* 4.0 a) c)
43.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	122	1001
1	307	907
2	1091	805
3	4573	795
done	5000	795

prune191.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

2.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify936.0ms

Counts

69 → 69

Iterations

Useful iterations: done (934.0ms)

Iter	Nodes	Cost
0	62	1075
1	150	969
2	520	881
3	2068	881
done	5000	878

prune248.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
177.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify828.0ms

Counts

166 → 166

Iterations

Useful iterations: done (823.0ms)

Iter	Nodes	Cost
0	256	5113
1	649	4541
2	2641	4211
done	5001	4209

prune634.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.4b

localize21.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
10.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`sqrt-prod`
8×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod` `add-log-exp`
7×	`pow1` `associate-r` `associate-/r*`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
146.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
176.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

161 → 161

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	261	4703
1	740	4091
2	2879	3625
done	5000	3623

prune400.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.4b

regimes265.0ms

Accuracy

96.5% (0.8b remaining)

Error of 11.9b against oracle of 11.1b and baseline of 34.2b

bsearch218.0ms

Steps

Iters	Range	Point
7	2.7208697733301495e+159	4.8169665308125605e+160	2.7494607386129675e+159
10	8.653734362945753e-196	5.147670875442886e-182	4.8356294076712185e-189
11	-1.829086240692416e+154	-2.187052964502477e+134	-1.3358786167585806e+154

Iters

Range

Point

2.7208697733301495e+159

4.8169665308125605e+160

2.7494607386129675e+159

8.653734362945753e-196

5.147670875442886e-182

4.8356294076712185e-189

-1.829086240692416e+154

-2.187052964502477e+134

-1.3358786167585806e+154

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	42	93
1	53	91
done	53	91

end0.0ms

sample1.2s

Algorithm

intervals

Results

256.0ms	1104×	body	2560	valid
237.0ms	5868×	body	80	valid
174.0ms	910×	body	1280	valid
111.0ms	2861×	body	80	nan
62.0ms	422×	body	640	valid
27.0ms	96×	body	5120	valid
23.0ms	212×	body	320	valid
9.0ms	120×	body	160	valid