Details

Time bar (total: 18.5s)

sample95.0ms

Algorithm
intervals
Results
22.0ms24×body1280valid
20.0ms42×body2560valid
17.0ms173×body80valid
7.0ms19×body640valid
6.0ms69×body80nan
3.0ms11×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify185.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
88.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
64.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
94.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms
(- (* b b) (* 4.0 (* a c)))
128.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
169 → 169
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02436690
15874705
217513760
done50003113

prune515.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (pow b 2) (* 4.0 (* a c)))
2.4b
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.8b
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite413.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
60×*-un-lft-identity
40×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
8×fma-neg prod-diff
7×cbrt-undiv div-exp associate-/r*
6×unpow-prod-down associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod unpow2 sqr-pow
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 162
Calls
4 calls:
38.0ms
(- (pow b 2) (* 4.0 (* a c)))
232.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
111.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
19.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series753.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (pow b 2) (* 4.0 (* a c)))
294.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
288.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
99.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify2.5s

Counts
174 → 174
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02824848
16874314
228373973
done50003960

prune720.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (pow b 2) (* 4.0 (* a c)))
2.5b
(* (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.8b
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite479.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×add-exp-log
46×*-un-lft-identity
40×times-frac
32×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp
14×difference-of-squares
10×sqrt-prod
8×cbrt-undiv fma-neg prod-diff cbrt-unprod
7×pow1 associate-*r* distribute-lft-out--
6×unpow-prod-down associate-/r* add-log-exp
4×expm1-log1p-u rec-exp flip3-- 1-exp associate-/r/ flip-- log1p-expm1-u
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unpow2 unswap-sqr sqr-pow
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 → 160
Calls
4 calls:
37.0ms
(- (pow b 2) (* 4.0 (* a c)))
253.0ms
(* (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
153.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
23.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (pow b 2) (* 4.0 (* a c)))
285.0ms
(* (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
300.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
86.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify2.0s

Counts
172 → 172
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02874566
17463970
230533501
done50013488

prune621.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
186.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
39.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
97.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
177 → 177
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02696947
16414848
219463851
done50003196

prune583.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.2b

regimes361.0ms

Accuracy

86.5% (3.7b remaining)

Error of 9.1b against oracle of 5.4b and baseline of 32.7b

bsearch349.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
9
9.448397398655464e-278
1.4829972419072586e-270
9.580019013081131e-278
9
-5.805813140116762e+38
-3.1089471099746935e+33
-7.631292124342714e+35

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
04369
15367
done5367

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.0s860×body1280valid
698.0ms5846×body80valid
623.0ms1102×body2560valid
363.0ms490×body640valid
314.0ms2941×body80nan
71.0ms107×body5120valid
65.0ms105×body160valid
58.0ms227×body320valid