Details

Time bar (total: 19.6s)

sample100.0ms

Algorithm
intervals
Results
21.0ms37×body2560valid
19.0ms191×body80valid
11.0ms23×body1280valid
8.0ms90×body80nan
5.0ms15×body640valid
1.0ms5×body160valid
1.0ms3×body320valid
1.0ms1×body5120valid

simplify277.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
312117
415317
516017
616417
done16417

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize42.0ms

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))))

rewrite314.0ms

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:
180.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms
(- (* b b) (* 4.0 (* a c)))
63.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
33.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
91.0ms
(- (* b b) (* 4.0 (* a c)))
152.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
130.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts
169 → 169
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02436690
16164729
224823764
done50023675

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize51.0ms

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))))

rewrite340.0ms

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:
205.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
35.0ms
(- (* b b) (* 4.0 (* a c)))
61.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series547.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
86.0ms
(- (* b b) (* 4.0 (* a c)))
142.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
136.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.0s

Counts
177 → 177
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02696947
16894918
230513859
done50003766

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize11.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune62.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.8b

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
8.0b
(/ (- (* b b) (fma b b (- (* (* a c) 4.0)))) (- (sqrt (- (* b b) (* (* a c) 4.0))) b))
18.7b
(- (* b b) (fma b b (- (* (* a c) 4.0))))
23.4b
(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
44×*-un-lft-identity
32×add-cube-cbrt
24×times-frac
21×prod-diff sqrt-prod
20×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-exp-log associate-/r* add-cbrt-cube distribute-lft-out--
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/ associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num fma-udef div-inv associate--r+
Counts
4 → 131
Calls
4 calls:
105.0ms
(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
127.0ms
(/ (- (* b b) (fma b b (- (* (* a c) 4.0)))) (- (sqrt (- (* b b) (* (* a c) 4.0))) b))
17.0ms
(- (* b b) (fma b b (- (* (* a c) 4.0))))
21.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

series775.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
369.0ms
(/ (- (* b b) (fma b b (- (* (* a c) 4.0)))) (- (sqrt (- (* b b) (* (* a c) 4.0))) b))
116.0ms
(- (* b b) (fma b b (- (* (* a c) 4.0))))
131.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

simplify2.8s

Counts
143 → 143
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02244259
16093860
229523042
done50003032

prune990.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.6b

regimes541.0ms

Accuracy

84.1% (4.5b remaining)

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

bsearch193.0ms

Steps
ItersRangePoint
8
4.049254448328916e+76
2.3057443967677173e+80
8.014692865739521e+79
5
-1.2210963557284012e-33
-3.582918381276583e-34
-3.8424248185280593e-34

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02941
13741
done3741

end0.0ms

sample4.2s

Algorithm
intervals
Results
832.0ms1110×body2560valid
761.0ms104×body5120valid
687.0ms5910×body80valid
513.0ms901×body1280valid
462.0ms3015×body80nan
155.0ms436×body640valid
57.0ms217×body320valid
20.0ms111×body160valid