Details

sample71.0ms

Algorithm

intervals

Results

16.0ms	37×	body	2560	valid
10.0ms	182×	body	80	valid
9.0ms	31×	body	1280	valid
5.0ms	89×	body	80	nan
5.0ms	22×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	5120	valid

simplify141.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	139
7	139
6	137
5	132
4	127
3	106
2	61
1	28
0	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `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 → 77

Calls

4 calls:

91.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
113.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(- (* b b) (* 4.0 (* a c)))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	4961
2	1246
1	402
0	155

prune625.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.4b	(- (* b b) (* 4.0 (* a c)))
6.1b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

16.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
7.0ms	(- (* b b) (* 4.0 (* a c)))
64.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
84.0ms	(- (* b b) (* 4.0 (* a c)))
143.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
101.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1246
1	419
0	163

prune676.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.4b	(- (* b b) (* 4.0 (* a c)))
10.8b	(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

62×	`times-frac`
38×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
30×	`add-cube-cbrt`
25×	`add-exp-log`
15×	`sqrt-prod`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`sqrt-div`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1` `div-inv`
5×	`cbrt-undiv`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*` `difference-of-squares`
2×	`sub-neg` `diff-log` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `frac-sub` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 122

Calls

4 calls:

28.0ms	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
7.0ms	(- (* b b) (* 4.0 (* a c)))
98.0ms	(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
58.0ms	(- (* b b) (* 4.0 (* a c)))
170.0ms	(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
103.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
2	1893
1	625
0	239

prune694.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

localize90.0ms

Local error

Found 4 expressions with local error:

22.7b	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
23.6b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.6b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.6b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite84.0ms

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` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

65.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
5.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
5.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
164.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
134.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
168.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
3	2008
2	724
1	351
0	188

prune745.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.2b

regimes550.0ms

Accuracy

84.5% (4.4b remaining)

Error of 10.5b against oracle of 6.1b and baseline of 34.5b

bsearch181.0ms

Steps

Iters	Range		Point
5	2.6243927093659187e+107	5.901159163981397e+107	4.8254787200880607e+107
9	-1.0952546209266604e-55	-7.034794544076098e-65	-9.332433396832084e-58

simplify11.0ms

Iterations

Iter	Nodes
done	35
1	35
0	28

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	1016×	body	2560	valid
815.0ms	892×	body	1280	valid
646.0ms	5891×	body	80	valid
203.0ms	2883×	body	80	nan
169.0ms	461×	body	640	valid
101.0ms	98×	body	5120	valid
79.0ms	118×	body	160	valid
52.0ms	220×	body	320	valid