Details

sample138.0ms

Algorithm

intervals

Results

14.0ms	179×	body	80	valid
13.0ms	36×	body	2560	valid
8.0ms	29×	body	1280	valid
4.0ms	79×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify74.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

195.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
150.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
136.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.9s

Counts

112 → 112

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	164	1638
1	385	1535
2	1102	1355
3	3175	1340
done	5001	1332

prune582.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (fma b_2 b_2 (* (- a) c)))) a)
0.6b	(+ (- b_2) (sqrt (fma b_2 b_2 (* (- a) c))))
0.8b	(fma b_2 b_2 (* (- a) c))
21.8b	(sqrt (fma b_2 b_2 (* (- a) c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out`
8×	`distribute-rgt-neg-in` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3-+` `sum-log` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `fma-udef` `div-inv`

Counts

4 → 92

Calls

4 calls:

51.0ms	(/ (+ (- b_2) (sqrt (fma b_2 b_2 (* (- a) c)))) a)
15.0ms	(+ (- b_2) (sqrt (fma b_2 b_2 (* (- a) c))))
0.0ms	(fma b_2 b_2 (* (- a) c))
2.0ms	(sqrt (fma b_2 b_2 (* (- a) c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (+ (- b_2) (sqrt (fma b_2 b_2 (* (- a) c)))) a)
131.0ms	(+ (- b_2) (sqrt (fma b_2 b_2 (* (- a) c))))
58.0ms	(fma b_2 b_2 (* (- a) c))
100.0ms	(sqrt (fma b_2 b_2 (* (- a) c)))

simplify3.0s

Counts

104 → 104

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	142	1490
1	317	1404
2	843	1243
3	2345	1228
done	5001	1225

prune439.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma b_2 b_2 (* (- a) c))
0.8b	(fma b_2 b_2 (* (- a) c))
21.8b	(sqrt (fma b_2 b_2 (* (- a) c)))
21.8b	(sqrt (fma b_2 b_2 (* (- a) c)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 50

Calls

4 calls:

1.0ms	(fma b_2 b_2 (* (- a) c))
1.0ms	(fma b_2 b_2 (* (- a) c))
3.0ms	(sqrt (fma b_2 b_2 (* (- a) c)))
3.0ms	(sqrt (fma b_2 b_2 (* (- a) c)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma b_2 b_2 (* (- a) c))
55.0ms	(fma b_2 b_2 (* (- a) c))
93.0ms	(sqrt (fma b_2 b_2 (* (- a) c)))
140.0ms	(sqrt (fma b_2 b_2 (* (- a) c)))

simplify2.1s

Counts

62 → 62

Iterations

Useful iterations: 4 (624.0ms)

Iter	Nodes	Cost
0	45	634
1	80	588
2	191	544
3	562	542
4	1640	540
done	5000	540

prune405.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series890.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt a)
212.0ms	(cbrt a)
311.0ms	(cbrt a)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.0s

Counts

68 → 68

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	75	470
1	170	427
2	449	392
3	1135	382
4	2565	381
done	5000	381

prune276.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.2b

regimes409.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.3b

bsearch85.0ms

Steps

Iters	Range		Point
5	1.8656011488683937e-53	5.89324344694736e-53	1.8920981354719558e-53
8	-3.0008378519073826e+120	-1.7813274366303991e+117	-1.0062396840173395e+118

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	36
1	30	36
2	34	36
3	35	36
done	35	36

end0.0ms

sample3.0s

Algorithm

intervals

Results

959.0ms	5910×	body	80	valid
531.0ms	1024×	body	2560	valid
364.0ms	2916×	body	80	nan
246.0ms	872×	body	1280	valid
138.0ms	467×	body	640	valid
114.0ms	125×	body	5120	valid
40.0ms	239×	body	320	valid
12.0ms	107×	body	160	valid