Details

Time bar (total: 16.5s)

sample121.0ms

Algorithm
intervals
Results
32.0ms18×body640valid
20.0ms39×body2560valid
15.0ms36×body1280valid
13.0ms166×body80valid
7.0ms90×body80nan
2.0ms10×body320valid
2.0ms4×body5120valid
0.0ms2×body160valid

simplify141.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
414117
515117
615517
done15517

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize14.0ms

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))))

rewrite135.0ms

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:
81.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
27.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
140.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
64.0ms
(- (* b b) (* 4.0 (* a c)))
89.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify940.0ms

Counts
89 → 89
Iterations

Useful iterations: done (936.0ms)

IterNodesCost
01571750
14181650
216411474
done50011466

prune418.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize36.0ms

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))))

rewrite342.0ms

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:
9.0ms
(- (* b b) (* 4.0 (* a c)))
172.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
135.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series766.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (* b b) (* 4.0 (* a c)))
263.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
322.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
112.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts
150 → 150
Iterations

Useful iterations: 2 (821.0ms)

IterNodesCost
02514460
16603964
240403668
done50013668

prune561.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize41.0ms

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))))

rewrite226.0ms

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:
100.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
83.0ms
(/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series1.3s

Counts
4 → 12
Calls
4 calls:
367.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
742.0ms
(/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
97.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
87.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify493.0ms

Counts
137 → 137
Iterations

Useful iterations: done (486.0ms)

IterNodesCost
02573763
17573366
done50002945

prune644.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
25×*-un-lft-identity
24×sqrt-pow1 sqrt-div
22×pow1
18×times-frac
17×add-cube-cbrt
11×pow1/2 sqrt-prod
9×flip3-- flip--
8×difference-of-squares
6×add-exp-log associate-/r* add-cbrt-cube
5×pow-prod-up
4×frac-times distribute-lft-out-- add-log-exp
3×rem-sqrt-square pow-prod-down pow-sqr associate-/l*
2×associate-*r/ associate-*l/ associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-2neg flip3-+ pow-plus div-exp clear-num flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
124.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c)))))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
42.0ms
(sqrt (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c))))))

series681.0ms

Counts
4 → 12
Calls
4 calls:
322.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c)))))) b))
99.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
126.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
134.0ms
(sqrt (* (sqrt (- (* b b) (* 4.0 (* a c)))) (sqrt (- (* b b) (* 4.0 (* a c))))))

simplify1.6s

Counts
117 → 117
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02023551
14542310
220772168
done50002166

prune564.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes428.0ms

Accuracy

82.2% (4.8b remaining)

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

bsearch297.0ms

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
03767
14467
done4467

end0.0ms

sample3.5s

Algorithm
intervals
Results
798.0ms5936×body80valid
705.0ms2934×body80nan
617.0ms1014×body2560valid
469.0ms912×body1280valid
142.0ms439×body640valid
64.0ms100×body5120valid
51.0ms232×body320valid
19.0ms122×body160valid