Details

Time bar (total: 15.6s)

sample35.0ms

Algorithm
intervals
Results
16.0ms271×body80valid

simplify102.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.7b
(- (* b c) (* a d))
24.2b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite61.0ms

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:
9.0ms
(+ (* c c) (* d d))
9.0ms
(- (* b c) (* a d))
42.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series211.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ (* c c) (* d d))
52.0ms
(- (* b c) (* a d))
112.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.2s

Counts
73 → 73
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01111202
13121070
21052961
33487961
done5000960

prune323.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.3b
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.3b
(fma b c (- (* d a)))
16.1b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite69.0ms

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:
11.0ms
(/ 1 (hypot c d))
42.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.0ms
(fma b c (- (* d a)))
5.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series593.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ 1 (hypot c d))
239.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
63.0ms
(fma b c (- (* d a)))
202.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify3.3s

Counts
142 → 142
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01542322
13562140
210981874
341361874
done50001840

prune459.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.3b
(fma b c (- (* d a)))
16.1b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×hypot-udef fma-udef associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot c d)
18.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.0ms
(fma b c (- (* d a)))
16.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series539.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(hypot c d)
218.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
70.0ms
(fma b c (- (* d a)))
171.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify1.9s

Counts
133 → 133
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01682712
13382650
27622455
325732401
done50002337

prune664.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (hypot c d))
0.6b
(cbrt (hypot c d))
6.0b
(/ (fma b c (- (* d a))) (cbrt (hypot c d)))
10.1b
(* (/ 1 (* (cbrt (hypot c d)) (cbrt (hypot c d)))) (/ (fma b c (- (* d a))) (cbrt (hypot c d))))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
51×add-exp-log times-frac
39×*-un-lft-identity
36×add-cube-cbrt
30×cbrt-prod
22×associate-*r*
20×prod-exp
19×add-cbrt-cube
16×div-exp
9×unswap-sqr
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×pow1 associate-/r*
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×pow1/3
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 139
Calls
4 calls:
1.0ms
(cbrt (hypot c d))
1.0ms
(cbrt (hypot c d))
10.0ms
(/ (fma b c (- (* d a))) (cbrt (hypot c d)))
104.0ms
(* (/ 1 (* (cbrt (hypot c d)) (cbrt (hypot c d)))) (/ (fma b c (- (* d a))) (cbrt (hypot c d))))

series971.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(cbrt (hypot c d))
136.0ms
(cbrt (hypot c d))
531.0ms
(/ (fma b c (- (* d a))) (cbrt (hypot c d)))
177.0ms
(* (/ 1 (* (cbrt (hypot c d)) (cbrt (hypot c d)))) (/ (fma b c (- (* d a))) (cbrt (hypot c d))))

simplify1.8s

Counts
151 → 151
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02123443
15323234
217632653
done50002515

prune543.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 5.2b

regimes276.0ms

Accuracy

35.2% (7.4b remaining)

Error of 13.1b against oracle of 5.6b and baseline of 17.1b

bsearch103.0ms

Steps
ItersRangePoint
8
2.0836639888440725e+105
3.6232372858298324e+108
1.3869240943923532e+108
10
-6.990724105819741e+111
-3.9220205095616873e+101
-1.0480538588897016e+111

simplify10.0ms

Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
02658
13746
24040
34434
done4434

end0.0ms

sample1.1s

Algorithm
intervals
Results
790.0ms8497×body80valid