Details

sample95.0ms

Algorithm

intervals

Results

35.0ms	30×	body	1280	valid
12.0ms	192×	body	80	valid
11.0ms	37×	body	2560	valid
5.0ms	81×	body	80	nan
3.0ms	12×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify72.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	107
5	107
4	99
3	79
2	44
1	24
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

86.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms	(- (* b b) (* 4.0 (* a c)))
30.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
77.0ms	(- (* b b) (* 4.0 (* a c)))
131.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
132.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify937.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1723
1	419
0	152

prune536.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
4.1b	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))) (* 2.0 a))
10.0b	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))
22.4b	(sqrt (- (pow b 2) (* 4.0 (* c a))))

rewrite319.0ms

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-cbrt-cube` `add-exp-log`
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×	`clear-num` `frac-2neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

31.0ms	(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
136.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))) (* 2.0 a))
130.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))
17.0ms	(sqrt (- (pow b 2) (* 4.0 (* c a))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
249.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))) (* 2.0 a))
262.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))
118.0ms	(sqrt (- (pow b 2) (* 4.0 (* c a))))

simplify1.8s

Counts

166 → 166

Iterations

Iter	Nodes
done	5002
2	3634
1	650
0	253

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
4.1b	(/ (/ (+ 0 (* 4.0 (* c a))) (* 1 (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))) (* 2.0 a))
10.0b	(/ (+ 0 (* 4.0 (* c a))) (* 1 (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))))
22.4b	(sqrt (- (pow b 2) (* 4.0 (* c a))))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

47.0ms	(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
58.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (* 1 (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))) (* 2.0 a))
78.0ms	(/ (+ 0 (* 4.0 (* c a))) (* 1 (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))))
22.0ms	(sqrt (- (pow b 2) (* 4.0 (* c a))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))
256.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (* 1 (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a))))))) (* 2.0 a))
243.0ms	(/ (+ 0 (* 4.0 (* c a))) (* 1 (- (- b) (sqrt (- (pow b 2) (* 4.0 (* c a)))))))
82.0ms	(sqrt (- (pow b 2) (* 4.0 (* c a))))

simplify2.0s

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
2	4135
1	641
0	231

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* c a)))
0.9b	(+ b (sqrt (- (* b b) (* 4.0 (* c a)))))
12.7b	(/ (* 4.0 (* c a)) a)
22.4b	(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 62

Calls

4 calls:

7.0ms	(- (* b b) (* 4.0 (* c a)))
13.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* c a)))))
30.0ms	(/ (* 4.0 (* c a)) a)
20.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* b b) (* 4.0 (* c a)))
101.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* c a)))))
17.0ms	(/ (* 4.0 (* c a)) a)
92.0ms	(sqrt (- (* b b) (* 4.0 (* c a))))

simplify1.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	2291
1	374
0	134

prune466.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

regimes464.0ms

Accuracy

94.4% (1.3b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 29.6b

bsearch236.0ms

Steps

Iters	Range	Point
9	3.768382185355077e+69	1.107955803311012e+78	4.2871760960662547e+77
3	-5.1570355596853615e-201	-3.8052178173245655e-201	-4.565615297402514e-201
8	-1.0455781936591884e+110	-3.8601914758440924e+107	-3.828737593568667e+109

Iters

Range

Point

3.768382185355077e+69

1.107955803311012e+78

4.2871760960662547e+77

-5.1570355596853615e-201

-3.8052178173245655e-201

-4.565615297402514e-201

-1.0455781936591884e+110

-3.8601914758440924e+107

-3.828737593568667e+109

simplify12.0ms

Iterations

Iter	Nodes
done	60
2	60
1	59
0	46

end0.0ms

sample3.1s

Algorithm

intervals

Results

963.0ms	936×	body	1280	valid
604.0ms	5837×	body	80	valid
487.0ms	1070×	body	2560	valid
248.0ms	2814×	body	80	nan
164.0ms	453×	body	640	valid
48.0ms	94×	body	5120	valid
44.0ms	223×	body	320	valid
15.0ms	113×	body	160	valid