Details

Time bar (total: 19.8s)

sample119.0ms

Algorithm
intervals
Results
44.0ms32×body2560valid
17.0ms184×body80valid
14.0ms31×body1280valid
7.0ms84×body80nan
6.0ms17×body640valid
2.0ms3×body5120valid
2.0ms6×body320valid
0.0ms1×body160valid

simplify153.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
379
243
125
014

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
0.2b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
1.4b
(- (* b b) (* 4.0 (* c a)))
24.6b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 183
Calls
4 calls:
75.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
55.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
9.0ms
(- (* b b) (* 4.0 (* c a)))
17.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series577.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
141.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)
73.0ms
(- (* b b) (* 4.0 (* c a)))
143.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify2.5s

Counts
195 → 195
Iterations
IterNodes
done5003
22338
1802
0321

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize62.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* 4.0 (* c a)))
24.6b
(sqrt (- (* b b) (* 4.0 (* c a))))
24.6b
(sqrt (- (* b b) (* 4.0 (* c a))))
24.6b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 67
Calls
4 calls:
12.0ms
(- (* b b) (* 4.0 (* c a)))
18.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
17.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
23.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series436.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (* b b) (* 4.0 (* c a)))
121.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
105.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
121.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify2.6s

Counts
79 → 79
Iterations
IterNodes
done5000
32471
2580
1182
071

prune888.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize101.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* 4.0 (* c a)))
24.6b
(sqrt (- (* b b) (* 4.0 (* c a))))
24.6b
(sqrt (- (* b b) (* 4.0 (* c a))))
24.6b
(sqrt (- (* b b) (* 4.0 (* c a))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 67
Calls
4 calls:
7.0ms
(- (* b b) (* 4.0 (* c a)))
16.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
22.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (* b b) (* 4.0 (* c a)))
127.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
140.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
100.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))

simplify2.4s

Counts
79 → 79
Iterations
IterNodes
done5000
32471
2580
1182
071

prune680.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize46.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (* (cbrt (- (* b b) (* 4.0 (* c a)))) (cbrt (- (* b b) (* 4.0 (* c a))))))
25.5b
(cbrt (- (* b b) (* 4.0 (* c a))))
25.5b
(cbrt (- (* b b) (* 4.0 (* c a))))
25.5b
(cbrt (- (* b b) (* 4.0 (* c a))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-- pow1/3 flip--
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u frac-times add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 74
Calls
4 calls:
33.0ms
(sqrt (* (cbrt (- (* b b) (* 4.0 (* c a)))) (cbrt (- (* b b) (* 4.0 (* c a))))))
5.0ms
(cbrt (- (* b b) (* 4.0 (* c a))))
6.0ms
(cbrt (- (* b b) (* 4.0 (* c a))))
8.0ms
(cbrt (- (* b b) (* 4.0 (* c a))))

series662.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(sqrt (* (cbrt (- (* b b) (* 4.0 (* c a)))) (cbrt (- (* b b) (* 4.0 (* c a))))))
167.0ms
(cbrt (- (* b b) (* 4.0 (* c a))))
158.0ms
(cbrt (- (* b b) (* 4.0 (* c a))))
159.0ms
(cbrt (- (* b b) (* 4.0 (* c a))))

simplify1.9s

Counts
86 → 86
Iterations
IterNodes
done5000
31876
2557
1225
0114

prune634.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.8b

regimes470.0ms

Accuracy

84.4% (4.5b remaining)

Error of 10.7b against oracle of 6.2b and baseline of 34.9b

bsearch228.0ms

Steps
ItersRangePoint
8
2.8373581988670566e-35
2.2677514638291856e-31
2.8983489306952693e-35
8
-2.748004767191833e+152
-7.260401024913698e+147
-2.221067196710922e+149

simplify6.0ms

Iterations
IterNodes
done32
132
028

end0.0ms

sample3.0s

Algorithm
intervals
Results
833.0ms5835×body80valid
502.0ms456×body640valid
476.0ms1040×body2560valid
346.0ms2881×body80nan
314.0ms906×body1280valid
121.0ms232×body320valid
78.0ms102×body5120valid
14.0ms116×body160valid