Details

sample129.0ms

Algorithm

intervals

Results

34.0ms	36×	body	2560	valid
29.0ms	187×	body	80	valid
20.0ms	26×	body	1280	valid
11.0ms	84×	body	80	nan
7.0ms	12×	body	640	valid
4.0ms	3×	body	5120	valid
4.0ms	8×	body	320	valid
2.0ms	5×	body	160	valid

simplify152.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.0b	(- (* b b) (* (* c a) 4))
1.0b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
23.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

75.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
15.0ms	(- (* b b) (* (* c a) 4))
39.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
11.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
73.0ms	(- (* b b) (* (* c a) 4))
112.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
99.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify684.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2001
2	1108
1	400
0	161

prune573.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
1.0b	(- (* b b) (* (* c a) 4))
1.0b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
23.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 166

Calls

4 calls:

57.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
7.0ms	(- (* b b) (* (* c a) 4))
38.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ 1 (/ a (- (sqrt (- (* b b) (* (* c a) 4))) b)))
60.0ms	(- (* b b) (* (* c a) 4))
100.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
98.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify871.0ms

Counts

178 → 178

Iterations

Iter	Nodes
done	2002
2	1756
1	651
0	265

prune698.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (+ (* -4 (* c a)) (* b b))) b)))
1.0b	(+ (* -4 (* c a)) (* b b))
1.0b	(- (sqrt (+ (* -4 (* c a)) (* b b))) b)
23.7b	(sqrt (+ (* -4 (* c a)) (* b b)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`flip3--` `div-inv` `flip--`
4×	`insert-posit16`
3×	`cbrt-undiv` `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` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 165

Calls

4 calls:

78.0ms	(/ 1 (/ a (- (sqrt (+ (* -4 (* c a)) (* b b))) b)))
15.0ms	(+ (* -4 (* c a)) (* b b))
77.0ms	(- (sqrt (+ (* -4 (* c a)) (* b b))) b)
16.0ms	(sqrt (+ (* -4 (* c a)) (* b b)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (/ a (- (sqrt (+ (* -4 (* c a)) (* b b))) b)))
60.0ms	(+ (* -4 (* c a)) (* b b))
86.0ms	(- (sqrt (+ (* -4 (* c a)) (* b b))) b)
84.0ms	(sqrt (+ (* -4 (* c a)) (* b b)))

simplify810.0ms

Counts

177 → 177

Iterations

Iter	Nodes
done	2001
2	1655
1	613
0	252

prune820.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
1.0b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
23.7b	(sqrt (- (* b b) (* (* c a) 4)))
23.7b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

40.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
47.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
12.0ms	(sqrt (- (* b b) (* (* c a) 4)))
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
97.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
87.0ms	(sqrt (- (* b b) (* (* c a) 4)))
89.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify555.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2000
2	589
1	195
0	82

prune456.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.1b

regimes407.0ms

Accuracy

84.6% (4.4b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 33.9b

bsearch561.0ms

Steps

Iters	Range		Point
8	2.469533614662255e-16	6.384179586440732e-13	5.297236684235463e-16
9	2.201345904528094e-30	9.673336284784144e-25	1.8656332031849816e-25
10	5.0092461758030895e-88	5.0325836698121444e-76	1.739098950628615e-79
9	-7.806260788625035e+148	-1.2289413495061505e+143	-1.6257289292067596e+144

simplify24.0ms

Iterations

Iter	Nodes
done	60
1	60
0	47

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.7s	5761×	body	80	valid
1.3s	1103×	body	2560	valid
726.0ms	957×	body	1280	valid
498.0ms	2981×	body	80	nan
321.0ms	480×	body	640	valid
202.0ms	115×	body	5120	valid
98.0ms	223×	body	320	valid
67.0ms	128×	body	160	valid