Details

Time bar (total: 8.3s)

sample40.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
7.0ms35×body1280valid
6.0ms27×body2560valid
3.0ms87×body80nan
2.0ms12×body640valid
1.0ms7×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify80.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
311917
414117
514717
615017
done15017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

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:
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify589.0ms

Counts
169 → 169
Iterations

Useful iterations: done (583.0ms)

IterNodesCost
02436690
15784705
218103760
done50003759

prune497.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite85.0ms

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:
56.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
72.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify753.0ms

Counts
177 → 177
Iterations

Useful iterations: done (747.0ms)

IterNodesCost
02696947
16424848
221063851
done50003850

prune332.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite73.0ms

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:
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify598.0ms

Counts
169 → 169
Iterations

Useful iterations: done (584.0ms)

IterNodesCost
02436690
15784705
218103760
done50003759

prune306.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

20.5b
(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
21.2b
(cbrt (- (* b b) (* 4.0 (* a c))))
21.2b
(cbrt (- (* b b) (* 4.0 (* a c))))
21.2b
(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 97
Calls
4 calls:
36.0ms
(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
2.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
2.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
2.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

series352.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
95.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
93.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
94.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
109 → 109
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01923874
13543361
28512692
331572632
done50002631

prune319.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.5b

regimes255.0ms

Accuracy

83.8% (4.6b remaining)

Error of 10.5b against oracle of 5.9b and baseline of 34.5b

bsearch104.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
3.6627135292415903e+111
8
-4.854151311909829e-126
-9.294658666337375e-130
-4.7828589349284326e-126

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02739
13239
done3239

end0.0ms

sample1.2s

Algorithm
intervals
Results
285.0ms1110×body2560valid
243.0ms5789×body80valid
180.0ms885×body1280valid
122.0ms2998×body80nan
72.0ms448×body640valid
31.0ms253×body320valid
30.0ms101×body5120valid
10.0ms126×body160valid