Details

Time bar (total: 12.1s)

sample24.0ms

Algorithm
intervals
Results
11.0ms264×body80valid

simplify122.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize18.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (* b c) (* a d))
28.0b
(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite35.0ms

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:
14.0ms
(- (* b c) (* a d))
20.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

series507.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(- (* b c) (* a d))
451.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.3s

Counts
54 → 54
Iterations

Useful iterations: done (2.3s)

IterNodesCost
087931
1214906
2710807
32547807
done5000801

prune244.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.2b
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
1.2b
(- (* b c) (* a d))
18.9b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite70.0ms

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)
39.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
8.0ms
(- (* b c) (* a d))
19.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series452.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(hypot c d)
201.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
52.0ms
(- (* b c) (* a d))
148.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify1.8s

Counts
128 → 128
Iterations

Useful iterations: 2 (267.0ms)

IterNodesCost
01702225
14542076
215271817
done50001817

prune408.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
1.2b
(- (* b c) (* a d))
18.9b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite57.0ms

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 add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 131
Calls
4 calls:
0.0ms
(hypot c d)
25.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
8.0ms
(- (* b c) (* a d))
19.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series355.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(hypot c d)
131.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
46.0ms
(- (* b c) (* a d))
129.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify2.0s

Counts
143 → 143
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01932874
14522796
212512600
344892545
done50002540

prune434.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (hypot c d) b)
0.1b
(/ (- (/ c (/ (hypot c d) b)) (* d (/ a (hypot c d)))) (hypot c d))
7.0b
(* d (/ a (hypot c d)))
10.0b
(/ c (/ (hypot c d) b))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
103×times-frac
75×add-sqr-sqrt
70×add-cube-cbrt *-un-lft-identity
19×associate-/r*
18×add-exp-log add-cbrt-cube
13×associate-*r*
9×associate-/l*
8×div-inv
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* clear-num associate-/l/
2×associate-*r/ prod-exp cbrt-unprod unswap-sqr
1×flip3-- div-sub pow-prod-down associate-/r/ *-commutative frac-sub flip--
Counts
4 → 168
Calls
4 calls:
5.0ms
(/ (hypot c d) b)
109.0ms
(/ (- (/ c (/ (hypot c d) b)) (* d (/ a (hypot c d)))) (hypot c d))
14.0ms
(* d (/ a (hypot c d)))
9.0ms
(/ c (/ (hypot c d) b))

series599.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (hypot c d) b)
335.0ms
(/ (- (/ c (/ (hypot c d) b)) (* d (/ a (hypot c d)))) (hypot c d))
89.0ms
(* d (/ a (hypot c d)))
102.0ms
(/ c (/ (hypot c d) b))

simplify977.0ms

Counts
180 → 180
Iterations

Useful iterations: done (973.0ms)

IterNodesCost
02742734
15992622
218792424
done50002422

prune560.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01321
11719
done1719

end0.0ms

sample811.0ms

Algorithm
intervals
Results
488.0ms8474×body80valid