Details

sample163.0ms

Algorithm

intervals

Results

18.0ms	37×	body	2560	valid
17.0ms	192×	body	80	valid
11.0ms	30×	body	1280	valid
6.0ms	81×	body	80	nan
3.0ms	12×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite198.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `sum-log` `flip3-+` `flip3--` `sqrt-div` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `div-inv`

Counts

4 → 100

Calls

4 calls:

103.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
29.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
61.0ms	(- (* b_2 b_2) (* a c))
115.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1655
1	405
0	164

prune678.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
4.2b	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
9.7b	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
22.4b	(sqrt (fma a (- c) (* b_2 b_2)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
228×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
162×	`add-cube-cbrt`
64×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
45×	`associate-/l*`
33×	`distribute-lft-out`
16×	`neg-mul-1`
15×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/` `distribute-neg-frac`
7×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

4 → 289

Calls

4 calls:

11.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
89.0ms	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
44.0ms	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
3.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

series674.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
205.0ms	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
264.0ms	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
110.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

simplify665.0ms

Counts

301 → 301

Iterations

Iter	Nodes
done	5000
1	1066
0	420

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
0.9b	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
12.4b	(/ (* c a) a)
22.4b	(sqrt (fma a (- c) (pow b_2 2)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
44×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-lft-out`
8×	`associate-/l*`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod`
2×	`clear-num` `frac-2neg` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

36.0ms	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
11.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
15.0ms	(/ (* c a) a)
2.0ms	(sqrt (fma a (- c) (pow b_2 2)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
118.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
10.0ms	(/ (* c a) a)
93.0ms	(sqrt (fma a (- c) (pow b_2 2)))

simplify1.2s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	2395
1	472
0	185

prune855.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
0.1b	(* c (/ 1 (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
0.9b	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
22.4b	(sqrt (fma a (- c) (* b_2 b_2)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-l` `sqrt-prod` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 114

Calls

4 calls:

23.0ms	(/ 1 (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
52.0ms	(* c (/ 1 (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
11.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
3.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1 (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
256.0ms	(* c (/ 1 (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
136.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
124.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

simplify985.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1657
1	385
0	158

prune545.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.8b

regimes467.0ms

Accuracy

93.9% (1.4b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 29.5b

bsearch176.0ms

Steps

Iters	Range	Point
9	3.768382185355077e+69	1.107955803311012e+78	9.585324748779203e+76
3	-5.1570355596853615e-201	-3.8052178173245655e-201	-4.058683644017215e-201
10	-6.622314338184697e+74	-4.7924972520805885e+61	-2.063494556122609e+74

Iters

Range

Point

3.768382185355077e+69

1.107955803311012e+78

9.585324748779203e+76

-5.1570355596853615e-201

-3.8052178173245655e-201

-4.058683644017215e-201

-6.622314338184697e+74

-4.7924972520805885e+61

-2.063494556122609e+74

simplify9.0ms

Iterations

Iter	Nodes
done	49
3	49
2	47
1	42
0	34

end0.0ms

sample2.9s

Algorithm

intervals

Results

529.0ms	1071×	body	2560	valid
486.0ms	5835×	body	80	valid
462.0ms	222×	body	320	valid
397.0ms	935×	body	1280	valid
197.0ms	2813×	body	80	nan
159.0ms	454×	body	640	valid
89.0ms	94×	body	5120	valid
15.0ms	115×	body	160	valid