Details

Time bar (total: 19.4s)

sample90.0ms

Algorithm
intervals
Results
19.0ms39×body2560valid
14.0ms36×body1280valid
13.0ms166×body80valid
7.0ms89×body80nan
6.0ms18×body640valid
2.0ms10×body320valid
2.0ms4×body5120valid
0.0ms2×body160valid

simplify26.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01013
11913
23313
34613
44913
done4913

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite227.0ms

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:
125.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
43.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(- (* b_2 b_2) (* a c))
26.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
129.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
58.0ms
(- (* b_2 b_2) (* a c))
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
183 → 183
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02425993
15784337
221453551
done50033006

prune505.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
4.4b
(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
9.8b
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
22.6b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite189.0ms

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:
26.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
67.0ms
(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
71.0ms
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
3.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series877.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
289.0ms
(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
324.0ms
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
135.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.1s

Counts
229 → 229
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03136352
17525415
236275099
done50015039

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2))
4.4b
(/ (/ (+ 0 (* c a)) (+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2))) a)
9.8b
(/ (+ 0 (* c a)) (+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2)))
22.6b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
143×*-un-lft-identity
138×times-frac
76×add-sqr-sqrt
75×add-cube-cbrt
34×distribute-lft-out
24×associate-/l*
17×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r/
8×associate-/r* add-log-exp
7×flip3-+ flip-+
6×fma-def sqrt-prod div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg clear-num sum-log
1×+-commutative neg-sub0 associate-+r- rem-sqrt-square sqrt-pow1 pow1/2 unsub-neg neg-log
Counts
4 → 185
Calls
4 calls:
29.0ms
(+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2))
91.0ms
(/ (/ (+ 0 (* c a)) (+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2))) a)
52.0ms
(/ (+ 0 (* c a)) (+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2)))
3.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series817.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2))
287.0ms
(/ (/ (+ 0 (* c a)) (+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2))) a)
304.0ms
(/ (+ 0 (* c a)) (+ (sqrt (fma (- c) a (* b_2 b_2))) (- b_2)))
118.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.3s

Counts
197 → 197
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02595119
16654180
236133988
done50003981

prune725.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
4.4b
(* (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) (/ 1 a))
9.8b
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
22.6b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite168.0ms

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:
29.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
89.0ms
(* (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) (/ 1 a))
34.0ms
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
2.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
281.0ms
(* (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) (/ 1 a))
291.0ms
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
129.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify3.2s

Counts
183 → 183
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02594230
17243529
240233086
done50003084

prune597.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

regimes307.0ms

Accuracy

82.3% (4.8b remaining)

Error of 10.6b against oracle of 5.7b and baseline of 33.1b

bsearch182.0ms

Steps
ItersRangePoint
11
8.182113676652236e-12
2116652649.122401
2098867031.9345784
9
-2.767900526575846e-127
-1.0722121724991011e-133
-4.0408082703632894e-132
4
-2.14594256023029e+80
-1.5018560828312564e+80
-1.763516214274614e+80

simplify6.0ms

Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
03760
14360
24458
done4458

end0.0ms

sample2.6s

Algorithm
intervals
Results
745.0ms1015×body2560valid
460.0ms5936×body80valid
384.0ms912×body1280valid
252.0ms2930×body80nan
127.0ms438×body640valid
41.0ms100×body5120valid
40.0ms232×body320valid
13.0ms123×body160valid