Details

sample95.0ms

Algorithm

intervals

Results

20.0ms	37×	body	2560	valid
16.0ms	185×	body	80	valid
15.0ms	33×	body	1280	valid
7.0ms	81×	body	80	nan
7.0ms	20×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify275.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	120	17
4	145	17
5	152	17
6	156	17
done	156	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
60×	`prod-diff`
49×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r` `neg-log` `clear-num` `associate-/r` `-commutative` `div-inv`

Counts

4 → 161

Calls

4 calls:

19.0ms	(* 4.0 (* a c))
121.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
60.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
30.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 4.0 (* a c))
119.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
95.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

173 → 173

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	255	6590
1	623	4603
2	1834	3668
done	5001	3021

prune587.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.1b	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.8b	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite453.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
78×	`times-frac`
72×	`*-un-lft-identity`
50×	`add-cube-cbrt`
27×	`associate-/l*`
26×	`sqrt-prod`
22×	`difference-of-squares`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`fma-neg` `associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 173

Calls

4 calls:

108.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
213.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
98.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series766.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
246.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
309.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts

185 → 185

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	288	5475
1	706	4743
2	2615	4289
done	5000	4221

prune766.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize39.0ms

Local error

Found 4 expressions with local error:

17.1b	(fma (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c)))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b))
25.1b	(cbrt (- (* b b) (* 4.0 (* a c))))
25.1b	(cbrt (- (* b b) (* 4.0 (* a c))))
25.1b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

0.0ms	(fma (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c)))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(fma (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c)))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b))
160.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
145.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
142.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts

67 → 67

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	87	1442
1	197	1258
2	562	1121
3	1984	1103
done	5001	1076

prune595.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt` `prod-diff`
59×	`*-un-lft-identity`
47×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*` `add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1`
3×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 141

Calls

3 calls:

88.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
69.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series397.0ms

Counts

3 → 9

Calls

3 calls:

162.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
140.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

150 → 150

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	228	6424
1	560	4450
2	1648	3535
done	5000	2888

prune358.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

regimes428.0ms

Accuracy

85.1% (4.0b remaining)

Error of 9.6b against oracle of 5.6b and baseline of 32.3b

bsearch457.0ms

Steps

Iters	Range		Point
8	1.538525478595148e+72	6.402915924844171e+74	2.9725940607578363e+74
9	-7.826064039423189e-132	-1.1138670077130767e-140	-6.373481960958038e-132
6	-3.4377365604695865e-95	-7.852755480555329e-96	-9.940959811381676e-96
9	-5.194408462768213e+38	-1.5993742599293638e+29	-3.438870219673744e+36

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	46	100
1	53	98
done	53	98

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	5850×	body	80	valid
791.0ms	1054×	body	2560	valid
474.0ms	924×	body	1280	valid
244.0ms	502×	body	640	valid
222.0ms	2933×	body	80	nan
134.0ms	110×	body	5120	valid
50.0ms	207×	body	320	valid
16.0ms	108×	body	160	valid