Details

Time bar (total: 8.4s)

sample333.0ms

Algorithm
intervals
Results
6.0ms43×body1280valid
6.0ms176×body80valid
6.0ms29×body2560valid
3.0ms91×body80nan
2.0ms17×body640valid
2.0ms2×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify32.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347
done347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize12.0ms

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))
0.7b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

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:
68.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
23.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0389850
11366779
25001753
done5001753

prune280.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.3b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 284
Calls
4 calls:
30.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
81.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
56.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
145.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
175.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify138.0ms

Counts
296 → 296
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
09195579
139184508
250014505
done50014505

prune556.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.3b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.7b
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
170×*-un-lft-identity
162×times-frac
118×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
32×add-exp-log
28×associate-/r*
26×distribute-lft-out-- difference-of-squares
23×add-cbrt-cube
21×distribute-lft-neg-in
16×div-exp
10×cbrt-undiv fma-neg
8×add-log-exp
7×neg-mul-1
6×prod-exp div-inv
5×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×1-exp cbrt-unprod
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log associate-/r/ associate-/l/
Counts
4 → 258
Calls
4 calls:
30.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
45.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
37.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series474.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
183.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
158.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify116.0ms

Counts
270 → 270
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09864682
143183613
250013595
done50013595

prune486.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.7b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1872×add-sqr-sqrt
1871×*-un-lft-identity
1387×add-cube-cbrt
267×associate-/l*
242×distribute-lft-out-- difference-of-squares
154×sqrt-prod
142×distribute-rgt-neg-in
60×prod-diff
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
21×distribute-lft-neg-in
13×cbrt-undiv
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×associate-/r*
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 1226
Calls
4 calls:
30.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
142.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
112.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify262.0ms

Counts
1238 → 1238
Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
0446326936
1500225697
done500225697

prune2.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.8b

regimes192.0ms

Accuracy

87% (3.3b remaining)

Error of 9.3b against oracle of 6.0b and baseline of 31.6b

bsearch113.0ms

Steps
ItersRangePoint
6
1.7832086820360693e-70
1.5218306367540535e-69
1.4939193519306575e-69
7
-2.1441117259981213e-299
-4.768714874085129e-301
-5.331911540015065e-301
10
-1.2433634659052315e+163
-5.7824766130184975e+150
-6.371698442415157e+150

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04124
14124
done4124

end0.0ms

sample1.0s

Algorithm
intervals
Results
189.0ms5893×body80valid
173.0ms977×body2560valid
136.0ms931×body1280valid
92.0ms2863×body80nan
55.0ms481×body640valid
26.0ms98×body5120valid
19.0ms228×body320valid
6.0ms111×body160valid