Details

Time bar (total: 29.2s)

sample108.0ms

Algorithm
intervals
Results
57.0ms284×body80valid
32.0ms91×body80nan

simplify557.0ms

Counts
1 → 1
Iterations
IterNodes
8170
7170
6168
5164
4157
3132
276
139
020

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.0b

localize143.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.7b
(- (sqrt (fma c (* a -4) (* b b))) b)
22.9b
(sqrt (fma c (* a -4) (* b b)))
22.9b
(sqrt (fma c (* a -4) (* b b)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
10.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
8.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
2.0ms
(sqrt (fma c (* a -4) (* b b)))
2.0ms
(sqrt (fma c (* a -4) (* b b)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
142.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
142.0ms
(sqrt (fma c (* a -4) (* b b)))
99.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.2s

Counts
177 → 177
Iterations
IterNodes
32153
2837
1417
0194

prune3.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

localize192.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.7b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 155
Calls
4 calls:
44.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
30.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
95.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
81.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.8s

Counts
167 → 167
Iterations
IterNodes
33914
21206
1434
0181

prune3.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize133.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
3.7b
(/ c (/ b a))
3.8b
(/ (* 2 c) (* (- (/ c (/ b a)) b) 2))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
93×add-sqr-sqrt
92×*-un-lft-identity
88×add-cube-cbrt
76×times-frac
60×prod-diff
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in add-cbrt-cube add-exp-log
14×associate-/r*
10×fma-neg
8×add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×div-inv
5×pow1
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l*
3×flip3-- associate-/r/ flip--
2×clear-num frac-2neg sqrt-div diff-log associate-*l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log
Counts
4 → 208
Calls
4 calls:
37.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
12.0ms
(/ c (/ b a))
44.0ms
(/ (* 2 c) (* (- (/ c (/ b a)) b) 2))
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
34.0ms
(/ c (/ b a))
240.0ms
(/ (* 2 c) (* (- (/ c (/ b a)) b) 2))
125.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
220 → 220
Iterations
IterNodes
22928
1915
0363

prune4.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize181.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
3.8b
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (/ c (/ (cbrt b) (cbrt a)))) b) 2))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
52×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×add-cbrt-cube add-exp-log
10×fma-neg
8×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×cbrt-prod flip3-- flip--
2×sqrt-div diff-log associate-*l/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 times-frac pow1/2 pow1/3 neg-log div-inv associate-/l*
Counts
4 → 149
Calls
4 calls:
1.0ms
(cbrt a)
40.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
60.0ms
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (/ c (/ (cbrt b) (cbrt a)))) b) 2))
25.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series521.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(cbrt a)
116.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
71.0ms
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (/ c (/ (cbrt b) (cbrt a)))) b) 2))
91.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts
161 → 161
Iterations
IterNodes
22235
1642
0252

prune4.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

regimes581.0ms

Accuracy

94.1% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 21.9b

bsearch334.0ms

Steps
ItersRangePoint
8
6.45623811977989e+97
1.5556153764929518e+101
1.6529445176198465e+100
7
-1.8217288728729631e+111
-6.606823090402082e+109
-5.148407540792454e+110

simplify9.0ms

Iterations
IterNodes
247
147
038

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.0s8769×body80valid
665.0ms2978×body80nan