Details

Time bar (total: 24.6s)

sample106.0ms

Algorithm
intervals
Results
22.0ms37×body2560valid
19.0ms191×body80valid
12.0ms23×body1280valid
8.0ms90×body80nan
6.0ms15×body640valid
1.0ms5×body160valid
1.0ms3×body320valid
1.0ms1×body5120valid

simplify243.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
414117
515117
615517
done15517

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in 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 → 77
Calls
4 calls:
133.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
19.0ms
(- (* b b) (* 4.0 (* a c)))
59.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms
(- (* b b) (* 4.0 (* a c)))
149.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
129.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
89 → 89
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01571750
14181650
216441474
done50001466

prune711.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize56.0ms

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 b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in 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 → 85
Calls
4 calls:
213.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
18.0ms
(- (* b b) (* 4.0 (* a c)))
49.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
84.0ms
(- (* b b) (* 4.0 (* a c)))
136.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
140.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
97 → 97
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01832003
14921837
223981573
done50001569

prune657.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
12.5b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite465.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 141
Calls
4 calls:
89.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
213.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
129.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series1.0s

Counts
4 → 12
Calls
4 calls:
149.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
326.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
393.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
143.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.0s

Counts
153 → 153
Iterations

Useful iterations: 2 (957.0ms)

IterNodesCost
02504579
16494063
236203761
done50013761

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b
(* (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
12.5b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite557.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×add-exp-log
44×*-un-lft-identity
40×times-frac
28×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp difference-of-squares
11×sqrt-prod
8×cbrt-undiv cbrt-unprod distribute-lft-out--
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unswap-sqr
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 → 139
Calls
4 calls:
86.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
294.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
148.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series1.5s

Counts
4 → 12
Calls
4 calls:
631.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
335.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
403.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
141.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.9s

Counts
151 → 151
Iterations

Useful iterations: done (3.9s)

IterNodesCost
02554293
17483725
245583307
done50013291

prune983.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

regimes542.0ms

Accuracy

84.2% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 33.9b

bsearch215.0ms

Steps
ItersRangePoint
10
9.08791783933159e+82
5.750161104817302e+93
9.623020473898683e+86
5
-1.2210963557284012e-33
-3.582918381276583e-34
-3.8424248185280593e-34

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02839
13639
done3639

end0.0ms

sample4.2s

Algorithm
intervals
Results
816.0ms1110×body2560valid
758.0ms5910×body80valid
721.0ms436×body640valid
678.0ms901×body1280valid
378.0ms3015×body80nan
73.0ms104×body5120valid
59.0ms217×body320valid
20.0ms111×body160valid