Details

sample67.0ms

Algorithm

intervals

Results

16.0ms	41×	body	2560	valid
11.0ms	178×	body	80	valid
9.0ms	29×	body	1280	valid
6.0ms	93×	body	80	nan
5.0ms	17×	body	640	valid
1.0ms	1×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	2×	body	320	valid

simplify157.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	77
2	43
1	25
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a) 2.0)
1.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite199.0ms

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-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

86.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a) 2.0)
81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a) 2.0)
103.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
76.0ms	(- (* b b) (* (* 4.0 a) c))
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

195 → 195

Iterations

Iter	Nodes
done	5000
2	2259
1	792
0	320

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (/ (/ 1 a) 2.0))
1.7b	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
2.0b	(- (* b b) (* (* a c) 4.0))
23.9b	(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

179.0ms	(* (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (/ (/ 1 a) 2.0))
71.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
6.0ms	(- (* b b) (* (* a c) 4.0))
9.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (/ (/ 1 a) 2.0))
123.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
75.0ms	(- (* b b) (* (* a c) 4.0))
107.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

simplify2.0s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	2332
1	828
0	304

prune928.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) a) 2.0)
1.7b	(- (sqrt (- (* b b) (* c (* a 4.0)))) b)
2.0b	(- (* b b) (* c (* a 4.0)))
23.9b	(sqrt (- (* b b) (* c (* a 4.0))))

rewrite196.0ms

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-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

104.0ms	(/ (/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) a) 2.0)
53.0ms	(- (sqrt (- (* b b) (* c (* a 4.0)))) b)
13.0ms	(- (* b b) (* c (* a 4.0)))
15.0ms	(sqrt (- (* b b) (* c (* a 4.0))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (/ (- (sqrt (- (* b b) (* c (* a 4.0)))) b) a) 2.0)
121.0ms	(- (sqrt (- (* b b) (* c (* a 4.0)))) b)
57.0ms	(- (* b b) (* c (* a 4.0)))
100.0ms	(sqrt (- (* b b) (* c (* a 4.0))))

simplify2.1s

Counts

195 → 195

Iterations

Iter	Nodes
done	5001
2	2301
1	797
0	320

prune984.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.1b

localize49.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* b b) (* c (* a 4.0)))
23.1b	(fma (sqrt (sqrt (- (* b b) (* c (* a 4.0))))) (sqrt (sqrt (- (* b b) (* c (* a 4.0))))) (- b))
23.9b	(sqrt (- (* b b) (* c (* a 4.0))))
23.9b	(sqrt (- (* b b) (* c (* a 4.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 60

Calls

4 calls:

11.0ms	(- (* b b) (* c (* a 4.0)))
0.0ms	(fma (sqrt (sqrt (- (* b b) (* c (* a 4.0))))) (sqrt (sqrt (- (* b b) (* c (* a 4.0))))) (- b))
13.0ms	(sqrt (- (* b b) (* c (* a 4.0))))
14.0ms	(sqrt (- (* b b) (* c (* a 4.0))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* c (* a 4.0)))
138.0ms	(fma (sqrt (sqrt (- (* b b) (* c (* a 4.0))))) (sqrt (sqrt (- (* b b) (* c (* a 4.0))))) (- b))
107.0ms	(sqrt (- (* b b) (* c (* a 4.0))))
96.0ms	(sqrt (- (* b b) (* c (* a 4.0))))

simplify2.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	2630
2	630
1	206
0	88

prune488.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

regimes352.0ms

Accuracy

85.5% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.9b

bsearch218.0ms

Steps

Iters	Range		Point
10	8.767897341253802e-114	4.657027509742155e-104	4.6129908231112306e-104
9	-6.117539429929052e+154	-3.6285784997486435e+148	-3.2516568688411723e+152

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample3.1s

Algorithm

intervals

Results

958.0ms	902×	body	1280	valid
572.0ms	1115×	body	2560	valid
538.0ms	5809×	body	80	valid
244.0ms	454×	body	640	valid
241.0ms	2954×	body	80	nan
59.0ms	105×	body	5120	valid
50.0ms	126×	body	160	valid
42.0ms	210×	body	320	valid