Details

Time bar (total: 18.6s)

sample56.0ms

Algorithm
intervals
Results
13.0ms188×body80valid
8.0ms28×body2560valid
7.0ms29×body1280valid
4.0ms95×body80nan
3.0ms17×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
1.0ms6×body160valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11913
23313
34613
44913
done4913

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
131.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms
(- (* b_2 b_2) (* a c))
33.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series433.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
54.0ms
(- (* b_2 b_2) (* a c))
125.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
95.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
183 → 183
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02425993
15784337
221303551
done50003006

prune561.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
2.3b
(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
9.2b
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
23.0b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
164×add-sqr-sqrt
162×times-frac
129×*-un-lft-identity
95×add-cube-cbrt
34×difference-of-squares
32×sqrt-prod
27×associate-/l*
18×prod-diff
17×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
6×flip3-- fma-neg flip-- div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 217
Calls
4 calls:
11.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
47.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
43.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
7.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series797.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
276.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
301.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
103.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify1.9s

Counts
229 → 229
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03136352
17525415
236265099
done50005039

prune993.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
2.4b
(* (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) (/ 1 a))
9.2b
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
23.0b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
65×*-un-lft-identity
52×times-frac
47×add-cube-cbrt
28×add-exp-log
24×associate-*l*
23×sqrt-prod
18×prod-diff add-cbrt-cube
16×difference-of-squares
13×associate-*r*
9×div-exp
8×prod-exp distribute-lft-out--
7×pow1
6×fma-neg associate-/r* add-log-exp unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u associate-/r/ cbrt-unprod log1p-expm1-u
3×flip3-- flip-- div-inv associate-/l*
2×rec-exp 1-exp associate-/l/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 171
Calls
4 calls:
11.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
77.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) (/ 1 a))
61.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
3.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series773.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
225.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) (/ 1 a))
317.0ms
(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
114.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify3.1s

Counts
183 → 183
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02594230
17243529
240223086
done50013084

prune682.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* c a) a) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
1.6b
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
12.7b
(/ (* c a) a)
23.0b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
66×times-frac
61×*-un-lft-identity
43×add-cube-cbrt
24×sqrt-prod
18×add-exp-log prod-diff add-cbrt-cube difference-of-squares
9×associate-/r* div-inv distribute-lft-out--
8×associate-/l*
7×cbrt-undiv div-exp
6×fma-neg add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg prod-exp clear-num associate-/r/ flip-- cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 155
Calls
4 calls:
34.0ms
(/ (/ (* c a) a) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
20.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
17.0ms
(/ (* c a) a)
3.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series608.0ms

Counts
4 → 12
Calls
4 calls:
314.0ms
(/ (/ (* c a) a) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
155.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
11.0ms
(/ (* c a) a)
127.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify1.5s

Counts
167 → 167
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02243462
15642804
225422519
done50022464

prune569.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.0b

regimes221.0ms

Accuracy

82.3% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 29.3b

bsearch152.0ms

Steps
ItersRangePoint
7
1.2976235572645919e-73
6.718394677208045e-72
3.590122721216627e-73
7
-4.1637922183371475e+115
-1.3908068482385633e+114
-1.4374353640327304e+115

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02741
13335
23535
done3535

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s5788×body80valid
541.0ms1118×body2560valid
383.0ms918×body1280valid
229.0ms3035×body80nan
193.0ms464×body640valid
47.0ms103×body5120valid
40.0ms218×body320valid
15.0ms97×body160valid