Details

Time bar (total: 14.5s)

sample40.0ms

Algorithm
intervals
Results
19.0ms262×body80valid

simplify115.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
12114
24014
35614
47614
59014
69414
done9414

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.3b
(- (* b c) (* a d))
24.3b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite97.0ms

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:
17.0ms
(+ (* c c) (* d d))
17.0ms
(- (* b c) (* a d))
60.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series246.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ (* c c) (* d d))
62.0ms
(- (* b c) (* a d))
150.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.4s

Counts
73 → 73
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01111202
13361071
21767963
done5000961

prune332.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.2b
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
14.7b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
43×times-frac
35×*-un-lft-identity
33×add-cube-cbrt
31×add-exp-log
19×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
6×pow1 cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×cbrt-unprod div-inv
3×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
3 → 120
Calls
3 calls:
6.0ms
(/ 1 (hypot c d))
24.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
11.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series611.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(/ 1 (hypot c d))
284.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
224.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify2.4s

Counts
129 → 129
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01492208
14042100
228741792
done50001774

prune474.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
14.7b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
52×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
9×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×cbrt-undiv div-exp
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 101
Calls
2 calls:
30.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
8.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series334.0ms

Counts
2 → 6
Calls
2 calls:
164.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
170.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify914.0ms

Counts
107 → 107
Iterations

Useful iterations: done (910.0ms)

IterNodesCost
01562538
13492478
216142311
done50012267

prune406.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1 (hypot c d)))
0.3b
(* (sqrt (/ 1 (hypot c d))) (* (sqrt (/ 1 (hypot c d))) (/ (fma b c (- (* d a))) (hypot c d))))
0.3b
(* (sqrt (/ 1 (hypot c d))) (/ (fma b c (- (* d a))) (hypot c d)))
14.7b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
55×times-frac
45×*-un-lft-identity sqrt-prod
42×add-cube-cbrt
32×associate-*l*
20×add-exp-log add-cbrt-cube
14×associate-*r*
13×pow1
11×sqrt-div
8×unswap-sqr
7×prod-exp cbrt-unprod
6×frac-times associate-*r/
5×div-inv
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 div-exp associate-/r* associate-/l*
2×*-commutative
1×pow-flip frac-2neg pow1/2 clear-num inv-pow
Counts
4 → 156
Calls
4 calls:
4.0ms
(sqrt (/ 1 (hypot c d)))
86.0ms
(* (sqrt (/ 1 (hypot c d))) (* (sqrt (/ 1 (hypot c d))) (/ (fma b c (- (* d a))) (hypot c d))))
41.0ms
(* (sqrt (/ 1 (hypot c d))) (/ (fma b c (- (* d a))) (hypot c d)))
11.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series859.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(sqrt (/ 1 (hypot c d)))
269.0ms
(* (sqrt (/ 1 (hypot c d))) (* (sqrt (/ 1 (hypot c d))) (/ (fma b c (- (* d a))) (hypot c d))))
329.0ms
(* (sqrt (/ 1 (hypot c d))) (/ (fma b c (- (* d a))) (hypot c d)))
170.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify3.4s

Counts
168 → 168
Iterations

Useful iterations: done (3.4s)

IterNodesCost
02353581
15843192
237482865
done50012857

prune936.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

regimes279.0ms

Accuracy

14.2% (9.8b remaining)

Error of 15.6b against oracle of 5.8b and baseline of 17.2b

bsearch38.0ms

Steps
ItersRangePoint
6
4.8641680594845535e+57
6.917141905494778e+58
6.766976291716989e+58

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01626
12326
22526
done2526

end0.0ms

sample1.2s

Algorithm
intervals
Results
733.0ms8444×body80valid