Details

sample75.0ms

Algorithm

intervals

Results

17.0ms	35×	body	2560	valid
14.0ms	188×	body	80	valid
10.0ms	28×	body	1280	valid
6.0ms	85×	body	80	nan
4.0ms	14×	body	640	valid
3.0ms	5×	body	5120	valid
3.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
0.8b	(- (* b b) (* (* 4 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite155.0ms

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:

96.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
15.0ms	(- (* b b) (* (* 4 a) c))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
58.0ms	(- (* b b) (* (* 4 a) c))
86.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
81.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1358
1	406
0	153

prune606.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
0.8b	(- (* b b) (* (* 4 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite180.0ms

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×	`associate-l`
4×	`insert-posit16` `distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`frac-times` `sum-log` `distribute-rgt-neg-in` `flip3--` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `associate-+l-` `div-inv`

Counts

4 → 84

Calls

4 calls:

102.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
11.0ms	(- (* b b) (* (* 4 a) c))
46.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (/ 1/2 a))
51.0ms	(- (* b b) (* (* 4 a) c))
98.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
110.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1787
1	469
0	178

prune549.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize46.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `distribute-rgt-neg-in` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 64

Calls

4 calls:

47.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
100.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
121.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
106.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	2649
2	693
1	219
0	84

prune567.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

localize55.0ms

Local error

Found 4 expressions with local error:

21.2b	(sqrt (* (* (cbrt (- (* b b) (* (* 4 a) c))) (cbrt (- (* b b) (* (* 4 a) c)))) (cbrt (- (* b b) (* (* 4 a) c)))))
22.0b	(cbrt (- (* b b) (* (* 4 a) c)))
22.0b	(cbrt (- (* b b) (* (* 4 a) c)))
22.0b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 93

Calls

4 calls:

137.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4 a) c))) (cbrt (- (* b b) (* (* 4 a) c)))) (cbrt (- (* b b) (* (* 4 a) c)))))
19.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4 a) c))) (cbrt (- (* b b) (* (* 4 a) c)))) (cbrt (- (* b b) (* (* 4 a) c)))))
145.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
140.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
127.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	1994
2	721
1	350
0	188

prune647.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.7b

regimes395.0ms

Accuracy

82.2% (5.1b remaining)

Error of 10.5b against oracle of 5.5b and baseline of 34.1b

bsearch112.0ms

Steps

Iters	Range		Point
6	1.5727591416233446e-143	1.789606490082599e-142	1.6528810740721013e-142
6	-2.971125736392027e+46	-1.937449214055594e+45	-2.900769547116861e+46

simplify9.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample3.1s

Algorithm

intervals

Results

659.0ms	2988×	body	80	nan
646.0ms	1083×	body	2560	valid
556.0ms	5804×	body	80	valid
533.0ms	932×	body	1280	valid
153.0ms	489×	body	640	valid
101.0ms	247×	body	320	valid
90.0ms	121×	body	160	valid
63.0ms	107×	body	5120	valid