Details

sample119.0ms

Algorithm

intervals

Results

36.0ms	191×	body	80	valid
23.0ms	37×	body	2560	valid
15.0ms	30×	body	1280	valid
10.0ms	103×	body	80	nan
6.0ms	16×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify123.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.4b	(- (* b b) (* (* 4 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite181.0ms

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*`
4×	`insert-posit16`
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 → 74

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
16.0ms	(- (* b b) (* (* 4 a) c))
45.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
65.0ms	(- (* b b) (* (* 4 a) c))
102.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
87.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.4s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1358
1	406
0	153

prune495.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (+ (* (* a c) -4) (* b b)))) (* 2 a))
0.4b	(+ (* (* a c) -4) (* b b))
1.6b	(+ (- b) (sqrt (+ (* (* a c) -4) (* b b))))
21.3b	(sqrt (+ (* (* a c) -4) (* b b)))

rewrite295.0ms

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*`
4×	`flip3-+` `flip-+` `insert-posit16`
3×	`sum-log` `distribute-rgt-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `+-commutative` `sqrt-div` `div-exp` `associate-+l-` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 73

Calls

4 calls:

181.0ms	(/ (+ (- b) (sqrt (+ (* (* a c) -4) (* b b)))) (* 2 a))
17.0ms	(+ (* (* a c) -4) (* b b))
68.0ms	(+ (- b) (sqrt (+ (* (* a c) -4) (* b b))))
25.0ms	(sqrt (+ (* (* a c) -4) (* b b)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (+ (- b) (sqrt (+ (* (* a c) -4) (* b b)))) (* 2 a))
78.0ms	(+ (* (* a c) -4) (* b b))
104.0ms	(+ (- b) (sqrt (+ (* (* a c) -4) (* b b))))
139.0ms	(sqrt (+ (* (* a c) -4) (* b b)))

simplify1.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	1267
1	405
0	147

prune430.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (+ (* (* a c) -4) (* b b)))) (/ 1/2 a))
0.4b	(+ (* (* a c) -4) (* b b))
1.6b	(+ (- b) (sqrt (+ (* (* a c) -4) (* b b))))
21.3b	(sqrt (+ (* (* a c) -4) (* b b)))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
5×	`flip3-+` `associate-l` `flip-+`
4×	`insert-posit16` `distribute-lft-out`
3×	`sum-log` `sqrt-prod`
2×	`frac-times` `+-commutative` `distribute-rgt-neg-in` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `associate-+l-` `div-inv`

Counts

4 → 83

Calls

4 calls:

265.0ms	(* (+ (- b) (sqrt (+ (* (* a c) -4) (* b b)))) (/ 1/2 a))
32.0ms	(+ (* (* a c) -4) (* b b))
80.0ms	(+ (- b) (sqrt (+ (* (* a c) -4) (* b b))))
35.0ms	(sqrt (+ (* (* a c) -4) (* b b)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (+ (- b) (sqrt (+ (* (* a c) -4) (* b b)))) (/ 1/2 a))
62.0ms	(+ (* (* a c) -4) (* b b))
101.0ms	(+ (- b) (sqrt (+ (* (* a c) -4) (* b b))))
98.0ms	(sqrt (+ (* (* a c) -4) (* b b)))

simplify1.8s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1713
1	467
0	172

prune653.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* a 4) c))
0.4b	(/ (sqrt 1/2) a)
1.6b	(- (sqrt (- (* b b) (* (* a 4) c))) b)
21.3b	(sqrt (- (* b b) (* (* a 4) c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

17.0ms	(- (* b b) (* (* a 4) c))
13.0ms	(/ (sqrt 1/2) a)
59.0ms	(- (sqrt (- (* b b) (* (* a 4) c))) b)
14.0ms	(sqrt (- (* b b) (* (* a 4) c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* (* a 4) c))
57.0ms	(/ (sqrt 1/2) a)
106.0ms	(- (sqrt (- (* b b) (* (* a 4) c))) b)
119.0ms	(sqrt (- (* b b) (* (* a 4) c)))

simplify2.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5010
3	3647
2	927
1	326
0	156

prune508.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 7.8b

regimes552.0ms

Accuracy

81.2% (5.2b remaining)

Error of 10.8b against oracle of 5.6b and baseline of 33.0b

bsearch286.0ms

Steps

Iters	Range		Point
7	3.2723221096518622e-21	8.349665184990521e-19	3.325219738594455e-21
7	5.034617224646791e-70	8.084342686052032e-69	1.0350377446088803e-69
1	1.8923753200636452e-106	2.0232344302868159e-106	1.990519652731023e-106
8	-5.8501169415505e+41	-1.816545290760657e+37	-2.9862044966069494e+41

simplify8.0ms

Iterations

Iter	Nodes
done	45
1	45
0	37

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	5918×	body	80	valid
515.0ms	1071×	body	2560	valid
433.0ms	834×	body	1280	valid
238.0ms	3077×	body	80	nan
194.0ms	463×	body	640	valid
63.0ms	123×	body	5120	valid
52.0ms	241×	body	320	valid
17.0ms	122×	body	160	valid