Details

Time bar (total: 21.4s)

sample91.0ms

Algorithm
intervals
Results
17.0ms204×body80valid
15.0ms37×body1280valid
12.0ms25×body2560valid
12.0ms104×body80nan
4.0ms14×body640valid
1.0ms5×body320valid
1.0ms1×body5120valid
0.0ms3×body160valid

simplify44.0ms

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: 36.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite200.0ms

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:
103.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(- (* b_2 b_2) (* a c))
31.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
95.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms
(- (* b_2 b_2) (* a c))
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
183 → 183
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02425993
15784337
221453551
done50033006

prune537.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
3.4b
(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
11.3b
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
23.9b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite188.0ms

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:
25.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
72.0ms
(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
59.0ms
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
4.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series899.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
366.0ms
(/ (/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
288.0ms
(/ (+ 0 (* c a)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
106.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.2s

Counts
229 → 229
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03136352
17525415
236275099
done50015039

prune850.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
3.4b
(/ (* (+ 0 (* c a)) (/ 1 (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) a)
11.3b
(* (+ 0 (* c a)) (/ 1 (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)))
23.9b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
41×*-un-lft-identity
32×add-cube-cbrt
28×add-exp-log
24×associate-*r*
23×times-frac
19×sqrt-prod
18×prod-diff add-cbrt-cube
9×div-exp
8×prod-exp difference-of-squares
7×pow1
6×fma-neg associate-/l/ add-log-exp
5×cbrt-undiv
4×expm1-log1p-u frac-times flip3-+ associate-*l/ cbrt-unprod flip-+ log1p-expm1-u distribute-lft-out--
3×associate-*l* associate-/r* unswap-sqr
2×rec-exp flip3-- 1-exp associate-*r/ associate-/r/ un-div-inv flip-- div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 142
Calls
4 calls:
14.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
28.0ms
(/ (* (+ 0 (* c a)) (/ 1 (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) a)
94.0ms
(* (+ 0 (* c a)) (/ 1 (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)))
2.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series817.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
278.0ms
(/ (* (+ 0 (* c a)) (/ 1 (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) a)
300.0ms
(* (+ 0 (* c a)) (/ 1 (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)))
124.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify5.4s

Counts
154 → 154
Iterations

Useful iterations: done (5.4s)

IterNodesCost
02433260
16492562
245382182
done50002181

prune588.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.1b

localize42.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (/ (/ 1 (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) (* (cbrt a) (cbrt a))) (/ (/ (* c a) (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) (cbrt a)))
6.5b
(/ (* c a) (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)))
23.9b
(sqrt (fma (- c) a (* b_2 b_2)))
23.9b
(sqrt (fma (- c) a (* b_2 b_2)))

rewrite359.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
191×add-exp-log
176×add-sqr-sqrt
104×*-un-lft-identity
95×div-exp
94×associate-*r*
89×sqrt-prod
80×add-cbrt-cube
76×add-cube-cbrt
62×prod-exp
51×cbrt-undiv cbrt-prod
37×associate-*l*
34×cbrt-unprod
22×difference-of-squares
18×unswap-sqr
16×sqrt-div associate-/r/
11×distribute-lft-out--
10×div-inv
9×associate-/r*
8×pow1 rec-exp flip3-- 1-exp flip--
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 286
Calls
4 calls:
295.0ms
(* (/ (/ 1 (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) (* (cbrt a) (cbrt a))) (/ (/ (* c a) (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) (cbrt a)))
29.0ms
(/ (* c a) (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)))
2.0ms
(sqrt (fma (- c) a (* b_2 b_2)))
2.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

series1.2s

Counts
4 → 12
Calls
4 calls:
343.0ms
(* (/ (/ 1 (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) (* (cbrt a) (cbrt a))) (/ (/ (* c a) (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))) (cbrt a)))
596.0ms
(/ (* c a) (sqrt (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)))
110.0ms
(sqrt (fma (- c) a (* b_2 b_2)))
114.0ms
(sqrt (fma (- c) a (* b_2 b_2)))

simplify799.0ms

Counts
298 → 298
Iterations

Useful iterations: done (787.0ms)

IterNodesCost
048111917
1171911067
done50009798

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.1b

regimes333.0ms

Accuracy

88.6% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 33.4b

bsearch185.0ms

Steps
ItersRangePoint
8
1.051086597250448e+104
1.8086281629461872e+108
2.750597423682243e+107
9
-1.973755526415477e-151
-1.4597075490129595e-159
-3.2648782224884627e-158
6
-2.7008634656039713e+50
-1.797023714648992e+49
-2.186983581637579e+50

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04494
15294
done5294

end0.0ms

sample2.8s

Algorithm
intervals
Results
868.0ms1042×body2560valid
521.0ms5893×body80valid
366.0ms929×body1280valid
222.0ms2947×body80nan
146.0ms476×body640valid
80.0ms88×body5120valid
48.0ms231×body320valid
13.0ms108×body160valid