Details

Time bar (total: 14.4s)

sample117.0ms

Algorithm
intervals
Results
26.0ms196×body80valid
24.0ms29×body2560valid
20.0ms27×body1280valid
14.0ms99×body80nan
7.0ms14×body640valid
2.0ms6×body320valid
2.0ms2×body5120valid
1.0ms2×body160valid

simplify283.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize417.0ms

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))

rewrite90.0ms

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
52.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
14.0ms
(- (* b b) (* 4 (* a c)))
8.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series438.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
115.0ms
(sqrt (- (* b b) (* 4 (* a c))))
110.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
65.0ms
(- (* b b) (* 4 (* a c)))

simplify556.0ms

Counts
111 → 93

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.8b

localize37.0ms

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)))))))

rewrite92.0ms

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
37.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
33.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
13.0ms
(- (* b b) (* 4 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
99.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
95.0ms
(sqrt (- (* b b) (* 4 (* a c))))
56.0ms
(- (* b b) (* 4 (* a c)))

simplify794.0ms

Counts
189 → 141

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.7b

localize46.0ms

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)))

rewrite70.0ms

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
24.0ms
(- (* b b) (* 4 (* a c)))
17.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4 (* a c))))) (sqrt (sqrt (- (* b b) (* 4 (* a c)))))))
14.0ms
(sqrt (- (* b b) (* 4 (* a c))))
14.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4 (* a c))))) (sqrt (sqrt (- (* b b) (* 4 (* a c)))))))
110.0ms
(sqrt (- (* b b) (* 4 (* a c))))
102.0ms
(sqrt (- (* b b) (* 4 (* a c))))
84.0ms
(- (* b b) (* 4 (* a c)))

simplify326.0ms

Counts
84 → 73

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.7b

localize66.0ms

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)))

rewrite69.0ms

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
34.0ms
(/ (* 1/2 (- (* b b) (- (* b b) (* 4 (* a c))))) a)
16.0ms
(- (* b b) (- (* b b) (* 4 (* a c))))
10.0ms
(- (* b b) (* 4 (* a c)))
8.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series228.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(sqrt (- (* b b) (* 4 (* a c))))
58.0ms
(- (* b b) (* 4 (* a c)))
49.0ms
(- (* b b) (- (* b b) (* 4 (* a c))))
22.0ms
(/ (* 1/2 (- (* b b) (- (* b b) (* 4 (* a c))))) a)

simplify371.0ms

Counts
95 → 83

prune913.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.7b

regimes337.0ms

Accuracy

96.1% (0.9b remaining)

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

bsearch351.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.2s5901×body80valid
1.0s1054×body2560valid
727.0ms884×body1280valid
426.0ms2927×body80nan
257.0ms421×body640valid
110.0ms116×body5120valid
87.0ms229×body320valid
31.0ms118×body160valid