Details

Time bar (total: 18.3s)

sample68.0ms

Algorithm
intervals
Results
13.0ms90×body80nan
12.0ms39×body2560valid
9.0ms36×body1280valid
9.0ms166×body80valid
4.0ms18×body640valid
1.0ms4×body5120valid
1.0ms10×body320valid
0.0ms2×body160valid

simplify204.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
414117
515117
615517
done15517

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize21.0ms

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)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite198.0ms

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:
141.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
106.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(- (* b b) (* 4.0 (* a c)))
138.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify934.0ms

Counts
89 → 89
Iterations

Useful iterations: done (929.0ms)

IterNodesCost
01571750
14181650
216411474
done50011466

prune426.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
4.4b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.7b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite384.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×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 → 138
Calls
4 calls:
18.0ms
(- (* b b) (* 4.0 (* a c)))
200.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
130.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series814.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* b b) (* 4.0 (* a c)))
249.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
388.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
97.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1s

Counts
150 → 150
Iterations

Useful iterations: 2 (741.0ms)

IterNodesCost
02514460
16603964
240403668
done50013668

prune665.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize28.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (* 2.0 a) (/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
7.1b
(/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
42×times-frac
34×add-sqr-sqrt sqrt-prod
24×*-un-lft-identity associate-/r*
17×cbrt-undiv div-exp
16×add-cube-cbrt
13×prod-exp cbrt-unprod
10×sqrt-div
8×difference-of-squares
7×associate-/r/
6×pow1
5×flip3-- flip--
4×div-inv distribute-lft-out-- add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l*
Counts
4 → 125
Calls
4 calls:
119.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
98.0ms
(/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
28.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series1.5s

Counts
4 → 12
Calls
4 calls:
401.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
828.0ms
(/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
98.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
131.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify573.0ms

Counts
137 → 137
Iterations

Useful iterations: done (557.0ms)

IterNodesCost
02573763
17573366
done50002945

prune701.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* a c) 4.0))
4.4b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)) (* 2.0 a))
9.7b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* (* a c) 4.0))) b))
22.5b
(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×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 → 138
Calls
4 calls:
10.0ms
(- (* b b) (* (* a c) 4.0))
135.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)) (* 2.0 a))
92.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* (* a c) 4.0))) b))
9.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

series695.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* a c) 4.0))
231.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)) (* 2.0 a))
294.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* (* a c) 4.0))) b))
98.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

simplify2.2s

Counts
150 → 150
Iterations

Useful iterations: 2 (739.0ms)

IterNodesCost
02504460
16563964
238833660
done50013660

prune549.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes460.0ms

Accuracy

82.2% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 32.9b

bsearch335.0ms

Steps
ItersRangePoint
11
8.182113676652236e-12
2116652649.122401
2098867031.9345784
9
-2.767900526575846e-127
-1.0722121724991011e-133
-4.275041523480464e-132
4
-2.14594256023029e+80
-1.5018560828312564e+80
-1.763516214274614e+80

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03967
14667
done4667

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s1014×body2560valid
571.0ms5936×body80valid
434.0ms912×body1280valid
306.0ms2934×body80nan
194.0ms439×body640valid
121.0ms100×body5120valid
55.0ms232×body320valid
18.0ms122×body160valid