Details

Time bar (total: 16.5s)

sample118.0ms

Algorithm
intervals
Results
81.0ms289×body80valid
17.0ms86×body80nan

simplify177.0ms

Counts
1 → 1
Iterations
IterNodes
done170
7170
6168
5164
4157
3132
276
139
020

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.5b

localize147.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (fma c (* a -4) (* b b))) b)
0.9b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
25.0b
(sqrt (fma c (* a -4) (* b b)))
25.0b
(sqrt (fma c (* a -4) (* b b)))

rewrite30.0ms

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:
7.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
13.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
2.0ms
(sqrt (fma c (* a -4) (* b b)))
5.0ms
(sqrt (fma c (* a -4) (* b b)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
129.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
114.0ms
(sqrt (fma c (* a -4) (* b b)))
109.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.2s

Counts
177 → 177
Iterations
IterNodes
done2000
32000
2995
1426
0194

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.4b

localize173.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
0.5b
(- (sqrt (fma c (* a -4) (* b b))) b)
25.0b
(sqrt (fma c (* a -4) (* b b)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
134×add-sqr-sqrt
107×*-un-lft-identity
81×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/r*
18×prod-diff
13×distribute-lft-out--
8×add-cbrt-cube add-exp-log
6×fma-neg
5×div-inv add-log-exp
4×pow1
3×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u associate-/l*
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log associate-/r/ flip--
Counts
3 → 167
Calls
3 calls:
23.0ms
(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
15.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series526.0ms

Counts
3 → 9
Calls
3 calls:
282.0ms
(/ c (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
120.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
124.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.4s

Counts
176 → 176
Iterations
IterNodes
done2000
32000
21828
1657
0267

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.4b

localize132.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (fma c (* a -4) (* b b))) b)
4.3b
(* (/ a b) c)
4.5b
(/ (* 2 (- (* (/ a b) c) b)) (* 2 a))
25.0b
(sqrt (fma c (* a -4) (* b b)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
29×*-un-lft-identity
27×add-cube-cbrt
21×add-cbrt-cube add-exp-log
18×prod-diff
16×sqrt-prod
13×associate-*l*
11×times-frac
7×pow1
6×fma-neg prod-exp cbrt-unprod add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r*
2×flip3-- associate-*r/ div-inv flip-- difference-of-squares unswap-sqr associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down associate-*l/ *-commutative associate-/l* distribute-lft-out--
Counts
4 → 119
Calls
4 calls:
8.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
16.0ms
(* (/ a b) c)
45.0ms
(/ (* 2 (- (* (/ a b) c) b)) (* 2 a))
1.0ms
(sqrt (fma c (* a -4) (* b b)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
25.0ms
(* (/ a b) c)
64.0ms
(/ (* 2 (- (* (/ a b) c) b)) (* 2 a))
85.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.3s

Counts
131 → 131
Iterations
IterNodes
done2008
32008
21858
1509
0203

prune927.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.4b

localize203.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt b)
0.9b
(* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c))
4.5b
(/ (* 2 (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b)) (* 2 a))
25.0b
(sqrt (fma c (* a -4) (* b b)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
85×add-exp-log
51×add-cbrt-cube
41×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
10×pow1
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod pow-prod-down associate-*l/ associate-*r/ sqrt-prod
2×times-frac div-inv associate-/l/
1×frac-times rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 pow1/3 associate-*r* *-commutative flip-- associate-/l*
Counts
4 → 108
Calls
4 calls:
1.0ms
(cbrt b)
50.0ms
(* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c))
185.0ms
(/ (* 2 (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b)) (* 2 a))
2.0ms
(sqrt (fma c (* a -4) (* b b)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(cbrt b)
42.0ms
(* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c))
77.0ms
(/ (* 2 (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b)) (* 2 a))
122.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.2s

Counts
120 → 120
Iterations
IterNodes
done2001
22001
1608
0206

prune999.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.3b

regimes609.0ms

Accuracy

91.3% (0.8b remaining)

Error of 13.3b against oracle of 12.6b and baseline of 21.2b

bsearch190.0ms

Steps
ItersRangePoint
9
1.1500868835104234e+100
1.1016243770318365e+105
2.6220942974526774e+104

simplify15.0ms

Iterations
IterNodes
done35
135
032

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.2s8747×body80valid
514.0ms2996×body80nan