Details

sample104.0ms

Algorithm

intervals

Results

21.0ms	33×	body	1280	valid
19.0ms	184×	body	80	valid
17.0ms	31×	body	2560	valid
9.0ms	90×	body	80	nan
4.0ms	12×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify170.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	119	16
5	128	16
done	128	16

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize47.0ms

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)))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

197.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
22.0ms	(- (* b b) (* 4.0 (* a c)))
105.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series570.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
84.0ms	(- (* b b) (* 4.0 (* a c)))
148.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
134.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts

118 → 118

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	193	2476
1	517	2183
2	2160	1862
done	5000	1794

prune923.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite455.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

294.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
24.0ms	(- (* b b) (* 4.0 (* a c)))
100.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
30.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series620.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ 1 (* 2.0 a)))
97.0ms	(- (* b b) (* 4.0 (* a c)))
153.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
145.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.2s

Counts

127 → 127

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	219	2739
1	590	2382
2	2882	1975
done	5001	1901

prune868.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize47.0ms

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)))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

185.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
19.0ms	(- (* b b) (* 4.0 (* a c)))
103.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
90.0ms	(- (* b b) (* 4.0 (* a c)))
155.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
131.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts

118 → 118

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	193	2476
1	517	2183
2	2160	1862
done	5000	1794

prune863.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

107.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
17.0ms	(- (* b b) (* 4.0 (* a c)))
101.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
73.0ms	(- (* b b) (* 4.0 (* a c)))
138.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
125.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.3s

Counts

164 → 164

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	259	4025
1	671	3498
2	3253	3147
done	5002	3070

prune939.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

regimes537.0ms

Accuracy

82.7% (5.1b remaining)

Error of 10.5b against oracle of 5.4b and baseline of 34.6b

bsearch317.0ms

Steps

Iters	Range		Point
8	7.520261887413394e-140	8.544177483477188e-136	2.4581158795060287e-136
10	-6.623625638726693e+82	-6.4709084601913214e+72	-1.6581383089037873e+81

simplify16.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	31	46
1	41	40
2	44	40
done	44	40

end0.0ms

sample4.4s

Algorithm

intervals

Results

814.0ms	1065×	body	2560	valid
807.0ms	5800×	body	80	valid
701.0ms	908×	body	1280	valid
612.0ms	122×	body	5120	valid
392.0ms	2982×	body	80	nan
239.0ms	452×	body	640	valid
118.0ms	231×	body	320	valid
26.0ms	133×	body	160	valid