Details

Time bar (total: 15.5s)

sample53.0ms

Algorithm
intervals
Results
29.0ms270×body80valid

simplify81.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma c c (* d d))
0.5b
(- (* b c) (* a d))
25.4b
(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num fma-udef div-inv
Counts
3 → 58
Calls
3 calls:
1.0ms
(fma c c (* d d))
16.0ms
(- (* b c) (* a d))
33.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

series274.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(fma c c (* d d))
60.0ms
(- (* b c) (* a d))
170.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.8s

Counts
67 → 67
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0961039
12261011
2762892
32648892
done5001886

prune267.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot d c))
0.2b
(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
0.5b
(- (* b c) (* a d))
13.8b
(/ (- (* b c) (* a d)) (hypot d c))

rewrite85.0ms

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* add-log-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv
3×rec-exp 1-exp
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg pow-flip fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 139
Calls
4 calls:
5.0ms
(/ 1 (hypot d c))
45.0ms
(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
9.0ms
(- (* b c) (* a d))
21.0ms
(/ (- (* b c) (* a d)) (hypot d c))

series509.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ 1 (hypot d c))
215.0ms
(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
54.0ms
(- (* b c) (* a d))
158.0ms
(/ (- (* b c) (* a d)) (hypot d c))

simplify1.9s

Counts
151 → 151
Iterations

Useful iterations: 2 (332.0ms)

IterNodesCost
01772462
14682264
215591997
done50011997

prune437.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (hypot d c) b)
0.2b
(* (/ 1 (hypot d c)) (- (/ c (/ (hypot d c) b)) (/ (* a d) (hypot d c))))
7.1b
(/ c (/ (hypot d c) b))
7.8b
(/ (* a d) (hypot d c))

rewrite432.0ms

Algorithm
rewrite-expression-head
Rules
1289×times-frac
746×add-sqr-sqrt
733×*-un-lft-identity
730×add-cube-cbrt
616×prod-diff
310×distribute-rgt-in distribute-lft-in
152×div-inv
25×add-exp-log
21×add-cbrt-cube
19×associate-/r*
15×associate-/r/
13×associate-*l*
8×div-exp
7×cbrt-undiv associate-*r* associate-/l*
6×pow1
5×prod-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times frac-2neg associate-*r/ clear-num cbrt-unprod difference-of-squares unswap-sqr
2×sub-neg flip3-- frac-sub flip--
1×rec-exp 1-exp pow-prod-down associate-*l/ *-commutative distribute-lft-out--
Counts
4 → 791
Calls
4 calls:
9.0ms
(/ (hypot d c) b)
296.0ms
(* (/ 1 (hypot d c)) (- (/ c (/ (hypot d c) b)) (/ (* a d) (hypot d c))))
10.0ms
(/ c (/ (hypot d c) b))
11.0ms
(/ (* a d) (hypot d c))

series708.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (hypot d c) b)
416.0ms
(* (/ 1 (hypot d c)) (- (/ c (/ (hypot d c) b)) (/ (* a d) (hypot d c))))
111.0ms
(/ c (/ (hypot d c) b))
84.0ms
(/ (* a d) (hypot d c))

simplify2.3s

Counts
803 → 803
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0126550692
1305141751
done500033900

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
0.6b
(cbrt c)
1.3b
(* (- (/ d (hypot d c))) a)
2.8b
(/ (cbrt c) (/ (cbrt (hypot d c)) b))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
161×add-sqr-sqrt
159×add-cube-cbrt *-un-lft-identity
138×cbrt-prod
30×associate-*l*
22×associate-/r*
13×distribute-lft-neg-in distribute-rgt-neg-in
11×add-exp-log
10×div-inv
8×add-cbrt-cube
6×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r*
2×pow1/3
1×distribute-lft-neg-out neg-mul-1 frac-2neg pow-prod-down associate-*l/ prod-exp clear-num associate-/r/ *-commutative cbrt-unprod distribute-neg-frac unswap-sqr
Counts
4 → 252
Calls
4 calls:
1.0ms
(cbrt c)
1.0ms
(cbrt c)
23.0ms
(* (- (/ d (hypot d c))) a)
21.0ms
(/ (cbrt c) (/ (cbrt (hypot d c)) b))

series706.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(cbrt c)
192.0ms
(cbrt c)
101.0ms
(* (- (/ d (hypot d c))) a)
219.0ms
(/ (cbrt c) (/ (cbrt (hypot d c)) b))

simplify1.2s

Counts
264 → 264
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03934357
18074089
223383934
done50013924

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes184.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02874
13774
24074
34174
done4174

end0.0ms

sample858.0ms

Algorithm
intervals
Results
530.0ms8479×body80valid