Details

Time bar (total: 9.6s)

sample24.0ms

Algorithm
intervals
Results
12.0ms277×body80valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.8b
(- (* b c) (* a d))
26.6b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
3.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))
11.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series167.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ (* c c) (* d d))
41.0ms
(- (* b c) (* a d))
94.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify499.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
01111202
13111070
21155961
done5000961

prune224.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.2b
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.5b
(fma b c (- (* d a)))
15.5b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×frac-2neg clear-num
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef inv-pow
Counts
4 → 130
Calls
4 calls:
2.0ms
(/ 1 (hypot c d))
13.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.0ms
(fma b c (- (* d a)))
2.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series607.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ 1 (hypot c d))
187.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
44.0ms
(fma b c (- (* d a)))
321.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify2.2s

Counts
142 → 142
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01542322
13782140
211361874
346901874
done50001873

prune350.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.5b
(fma b c (- (* d a)))
15.5b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×fma-udef associate-/l/
Counts
3 → 111
Calls
3 calls:
6.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.0ms
(fma b c (- (* d a)))
2.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series319.0ms

Counts
3 → 9
Calls
3 calls:
137.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
44.0ms
(fma b c (- (* d a)))
137.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify1.4s

Counts
120 → 120
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01612652
13342592
29012403
331752349
done50002347

prune345.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot c d) (fma b c (- (* d a))))) (hypot c d))
0.3b
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
0.5b
(fma b c (- (* d a)))
15.5b
(/ (hypot c d) (fma b c (- (* d a))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 319
Calls
4 calls:
16.0ms
(/ (/ 1 (/ (hypot c d) (fma b c (- (* d a))))) (hypot c d))
5.0ms
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
0.0ms
(fma b c (- (* d a)))
2.0ms
(/ (hypot c d) (fma b c (- (* d a))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ (/ 1 (/ (hypot c d) (fma b c (- (* d a))))) (hypot c d))
121.0ms
(/ 1 (/ (hypot c d) (fma b c (- (* d a)))))
44.0ms
(fma b c (- (* d a)))
94.0ms
(/ (hypot c d) (fma b c (- (* d a))))

simplify1.5s

Counts
331 → 331
Iterations

Useful iterations: done (1.4s)

IterNodesCost
04599298
110818210
225197632
done50007560

prune568.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

regimes178.0ms

Accuracy

34.8% (7.2b remaining)

Error of 13.3b against oracle of 6.1b and baseline of 17.2b

bsearch68.0ms

Steps
ItersRangePoint
8
2.5697366854017785e+130
7.599228493726907e+133
6.190379428939819e+130
8
-3.636339513145555e+183
-6.025167878664677e+179
-1.022076645889743e+180

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01934
12534
22734
done2734

end0.0ms

sample500.0ms

Algorithm
intervals
Results
289.0ms8494×body80valid