Details

Time bar (total: 11.3s)

sample20.0ms

Algorithm
intervals
Results
9.0ms275×body80valid

simplify48.0ms

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: 22.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(- (* b c) (* a d))
22.3b
(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num div-inv
Counts
2 → 48
Calls
2 calls:
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

series138.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(- (* b c) (* a d))
94.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify1.1s

Counts
54 → 54
Iterations

Useful iterations: done (1.1s)

IterNodesCost
087931
1217906
2769807
32945807
done5000805

prune167.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.3b
(- (* b c) (* d a))
0.3b
(* (/ 1 (hypot c d)) (/ (- (* b c) (* d a)) (hypot c d)))
12.0b
(/ (- (* b c) (* d a)) (hypot c d))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 add-log-exp unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×associate-/r* div-inv associate-/l*
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg hypot-udef frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 116
Calls
4 calls:
0.0ms
(hypot c d)
3.0ms
(- (* b c) (* d a))
18.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* d a)) (hypot c d)))
10.0ms
(/ (- (* b c) (* d a)) (hypot c d))

series424.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(hypot c d)
46.0ms
(- (* b c) (* d a))
193.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* d a)) (hypot c d)))
137.0ms
(/ (- (* b c) (* d a)) (hypot c d))

simplify840.0ms

Counts
128 → 128
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
01692225
14902088
218611817
done50001817

prune373.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (fma b c (- (* a d))) (hypot c d)) (hypot c d))
0.3b
(fma b c (- (* a d)))
12.0b
(/ (fma b c (- (* a d))) (hypot c d))

rewrite13.0ms

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)
6.0ms
(/ (/ (fma b c (- (* a d))) (hypot c d)) (hypot c d))
0.0ms
(fma b c (- (* a d)))
2.0ms
(/ (fma b c (- (* a d))) (hypot c d))

series358.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(hypot c d)
129.0ms
(/ (/ (fma b c (- (* a d))) (hypot c d)) (hypot c d))
51.0ms
(fma b c (- (* a d)))
130.0ms
(/ (fma b c (- (* a d))) (hypot c d))

simplify2.2s

Counts
133 → 133
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01692712
13512650
211762455
340202401
done50012399

prune601.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (* (fma b c (- (* a d))) (/ 1 (hypot c d))) (hypot c d))
0.3b
(fma b c (- (* a d)))
12.1b
(* (fma b c (- (* a d))) (/ 1 (hypot c d)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
21×add-sqr-sqrt
18×add-cbrt-cube
15×*-un-lft-identity
14×add-cube-cbrt times-frac
13×associate-*r*
9×div-exp
8×prod-exp
6×pow1
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-*l* associate-/r* unswap-sqr
2×rec-exp 1-exp associate-*r/ un-div-inv div-inv associate-/l/
1×hypot-udef frac-2neg pow-prod-down clear-num *-commutative fma-udef associate-/l*
Counts
4 → 87
Calls
4 calls:
0.0ms
(hypot c d)
5.0ms
(/ (* (fma b c (- (* a d))) (/ 1 (hypot c d))) (hypot c d))
0.0ms
(fma b c (- (* a d)))
8.0ms
(* (fma b c (- (* a d))) (/ 1 (hypot c d)))

series345.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
127.0ms
(/ (* (fma b c (- (* a d))) (/ 1 (hypot c d))) (hypot c d))
45.0ms
(fma b c (- (* a d)))
126.0ms
(* (fma b c (- (* a d))) (/ 1 (hypot c d)))

simplify3.6s

Counts
99 → 99
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01281509
13141365
212431111
345411097
done50001097

prune257.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

regimes209.0ms

Accuracy

35.9% (6.7b remaining)

Error of 12.6b against oracle of 5.8b and baseline of 16.3b

bsearch69.0ms

Steps
ItersRangePoint
6
4.497054947537868e+154
5.359771339659149e+155
5.3202544266061094e+154
9
-9.04709806302392e+124
-4.4188440889263735e+116
-2.7774429101464625e+124

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02340
13134
23434
done3434

end0.0ms

sample492.0ms

Algorithm
intervals
Results
283.0ms8478×body80valid