Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify55.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	105	16
5	113	16
done	113	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
19×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

39.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts

195 → 195

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	319	4967
1	751	4592
2	2159	4283
done	5000	4264

prune531.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) (/ (/ 1 2.0) a))
1.0b	(fma b b (- (* 4.0 (* a c))))
1.3b	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
21.1b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`times-frac`
60×	`*-un-lft-identity`
55×	`add-cube-cbrt`
43×	`associate-r`
19×	`add-exp-log`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`add-cbrt-cube`
7×	`pow1`
6×	`fma-neg` `div-exp` `associate-l` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `flip3--` `flip--` `cbrt-unprod`
2×	`frac-times` `associate-*l/` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `fma-udef`

Counts

4 → 143

Calls

4 calls:

38.0ms	(* (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) (/ (/ 1 2.0) a))
0.0ms	(fma b b (- (* 4.0 (* a c))))
6.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
1.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) (/ (/ 1 2.0) a))
55.0ms	(fma b b (- (* 4.0 (* a c))))
89.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
82.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify846.0ms

Counts

155 → 155

Iterations

Useful iterations: done (837.0ms)

Iter	Nodes	Cost
0	282	3455
1	714	2972
2	1990	2592
done	5000	2565

prune407.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) 2.0) a)
1.0b	(fma b b (- (* 4.0 (* a c))))
1.3b	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
21.1b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-/r*`
2×	`div-sub`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `flip--` `fma-udef` `associate-/l/`

Counts

4 → 175

Calls

4 calls:

17.0ms	(/ (/ (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) 2.0) a)
0.0ms	(fma b b (- (* 4.0 (* a c))))
6.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
1.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (/ (- (sqrt (fma b b (- (* 4.0 (* a c))))) b) 2.0) a)
57.0ms	(fma b b (- (* 4.0 (* a c))))
91.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
81.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify767.0ms

Counts

187 → 187

Iterations

Useful iterations: done (761.0ms)

Iter	Nodes	Cost
0	297	4777
1	679	4427
2	1812	4136
done	5000	4113

prune505.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize19.0ms

Local error

Found 4 expressions with local error:

21.9b	(cbrt (fma b b (- (* 4.0 (* a c)))))
21.9b	(cbrt (fma b b (- (* 4.0 (* a c)))))
21.9b	(cbrt (fma b b (- (* 4.0 (* a c)))))
23.0b	(fma (sqrt (* (cbrt (fma b b (- (* 4.0 (* a c))))) (cbrt (fma b b (- (* 4.0 (* a c))))))) (sqrt (cbrt (fma b b (- (* 4.0 (* a c)))))) (- b))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt (fma b b (- (* 4.0 (* a c)))))
0.0ms	(cbrt (fma b b (- (* 4.0 (* a c)))))
1.0ms	(cbrt (fma b b (- (* 4.0 (* a c)))))
0.0ms	(fma (sqrt (* (cbrt (fma b b (- (* 4.0 (* a c))))) (cbrt (fma b b (- (* 4.0 (* a c))))))) (sqrt (cbrt (fma b b (- (* 4.0 (* a c)))))) (- b))

series443.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (fma b b (- (* 4.0 (* a c)))))
107.0ms	(cbrt (fma b b (- (* 4.0 (* a c)))))
109.0ms	(cbrt (fma b b (- (* 4.0 (* a c)))))
119.0ms	(fma (sqrt (* (cbrt (fma b b (- (* 4.0 (* a c))))) (cbrt (fma b b (- (* 4.0 (* a c))))))) (sqrt (cbrt (fma b b (- (* 4.0 (* a c)))))) (- b))

simplify884.0ms

Counts

61 → 61

Iterations

Useful iterations: 4 (341.0ms)

Iter	Nodes	Cost
0	72	1220
1	138	1066
2	303	956
3	750	938
4	2040	917
done	5001	917

prune268.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.3b

regimes211.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 33.8b

bsearch102.0ms

Steps

Iters	Range		Point
8	1.3679096689958957e-81	5.608239720335765e-77	3.84613441880261e-81
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	42
1	43	36
2	51	36
done	51	36

end0.0ms

sample1.2s

Algorithm

intervals

Results

258.0ms	1074×	body	2560	valid
239.0ms	5844×	body	80	valid
174.0ms	907×	body	1280	valid
112.0ms	2890×	body	80	nan
67.0ms	452×	body	640	valid
30.0ms	102×	body	5120	valid
26.0ms	234×	body	320	valid
9.0ms	119×	body	160	valid