Details

Time bar (total: 14.2s)

sample164.0ms

Algorithm
intervals
Results
33.0ms196×body80valid
32.0ms29×body2560valid
24.0ms2×body5120valid
23.0ms27×body1280valid
16.0ms99×body80nan
9.0ms14×body640valid
3.0ms6×body320valid
1.0ms2×body160valid

simplify223.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize26.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (- (* b b) (* 4 (* a c))))
0.9b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.6b
(- (* b b) (* 4 (* a c)))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×times-frac add-cube-cbrt associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- insert-posit16 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 clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 81
Calls
4 calls:
Slowest
46.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
108.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
91.0ms
(sqrt (- (* b b) (* 4 (* a c))))
70.0ms
(- (* b b) (* 4 (* a c)))

simplify498.0ms

Counts
111 → 93

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.8b

localize51.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (- (* b b) (* 4 (* a c))))
0.9b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.6b
(- (* b b) (* 4 (* a c)))
0.2b
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
4×insert-posit16
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log cbrt-unprod pow-flip inv-pow
Counts
4 → 129
Calls
4 calls:
Slowest
54.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4 (* a c))))
8.0ms
(- (* b b) (* 4 (* a c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
112.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
100.0ms
(sqrt (- (* b b) (* 4 (* a c))))
61.0ms
(- (* b b) (* 4 (* a c)))

simplify720.0ms

Counts
189 → 141

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.7b

localize57.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (- (* b b) (* 4 (* a c))))
21.7b
(sqrt (- (* b b) (* 4 (* a c))))
9.2b
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4 (* a c))))) (sqrt (sqrt (- (* b b) (* 4 (* a c)))))))
0.6b
(- (* b b) (* 4 (* a c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
9×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
3×diff-log
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log difference-of-squares
Counts
4 → 61
Calls
4 calls:
Slowest
16.0ms
(sqrt (- (* b b) (* 4 (* a c))))
8.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4 (* a c))))) (sqrt (sqrt (- (* b b) (* 4 (* a c)))))))
8.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series690.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
419.0ms
(sqrt (- (* b b) (* 4 (* a c))))
114.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4 (* a c))))) (sqrt (sqrt (- (* b b) (* 4 (* a c)))))))
100.0ms
(sqrt (- (* b b) (* 4 (* a c))))
56.0ms
(- (* b b) (* 4 (* a c)))

simplify293.0ms

Counts
84 → 73

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.7b

localize46.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (- (* b b) (* 4 (* a c))))
15.8b
(- (* b b) (- (* b b) (* 4 (* a c))))
7.4b
(/ (* 1/2 (- (* b b) (- (* b b) (* 4 (* a c))))) a)
0.6b
(- (* b b) (* 4 (* a c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
9×add-sqr-sqrt add-cbrt-cube add-exp-log
7×*-un-lft-identity add-cube-cbrt
5×pow1
4×flip3-- diff-log insert-posit16 flip--
3×associate-/r* sub-neg times-frac sqrt-prod
2×cbrt-undiv sqrt-div div-exp associate-*r/ associate--r+ associate-/l/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l* associate--r- difference-of-squares
Counts
4 → 71
Calls
4 calls:
Slowest
45.0ms
(/ (* 1/2 (- (* b b) (- (* b b) (* 4 (* a c))))) a)
16.0ms
(- (* b b) (- (* b b) (* 4 (* a c))))
8.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series183.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(sqrt (- (* b b) (* 4 (* a c))))
53.0ms
(- (* b b) (* 4 (* a c)))
25.0ms
(- (* b b) (- (* b b) (* 4 (* a c))))
15.0ms
(/ (* 1/2 (- (* b b) (- (* b b) (* 4 (* a c))))) a)

simplify451.0ms

Counts
95 → 83

prune994.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.7b

regimes360.0ms

Accuracy

96.1% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.1b

bsearch416.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.1s1054×body2560valid
846.0ms5901×body80valid
759.0ms421×body640valid
691.0ms884×body1280valid
463.0ms2927×body80nan
142.0ms229×body320valid
118.0ms116×body5120valid
34.0ms118×body160valid