Details

Time bar (total: 15.2s)

sample48.0ms

Algorithm
intervals
Results
25.0ms272×body80valid

simplify97.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.5b
(- (* b c) (* a d))
29.4b
(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite40.0ms

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:
15.0ms
(- (* b c) (* a d))
22.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

series190.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(- (* b c) (* a d))
139.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.5s

Counts
54 → 54
Iterations

Useful iterations: done (2.5s)

IterNodesCost
087931
1214906
2710807
32547807
done5000801

prune214.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.3b
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b
(- (* b c) (* a d))
17.6b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite96.0ms

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 c d))
46.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
9.0ms
(- (* b c) (* a d))
31.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series500.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ 1 (hypot c d))
230.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
49.0ms
(- (* b c) (* a d))
157.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify1.8s

Counts
151 → 151
Iterations

Useful iterations: 2 (319.0ms)

IterNodesCost
01772462
14682264
215591997
done50011997

prune457.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d)))
0.3b
(* (/ 1 (hypot c d)) (- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d))))
10.0b
(/ c (/ (hypot c d) b))
11.3b
(/ (* a d) (hypot c d))

rewrite553.0ms

Algorithm
rewrite-expression-head
Rules
1943×times-frac
1115×add-sqr-sqrt
1095×*-un-lft-identity
1090×add-cube-cbrt
924×prod-diff
310×distribute-rgt-in distribute-lft-in
227×div-inv
44×fma-neg
23×add-exp-log associate-/r/
19×add-cbrt-cube
16×associate-/r*
13×associate-*l*
7×div-exp associate-*r*
6×pow1 cbrt-undiv add-log-exp difference-of-squares
5×prod-exp
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×frac-times sub-neg flip3-- associate-*r/ frac-sub flip-- cbrt-unprod unswap-sqr
2×frac-2neg clear-num distribute-lft-out--
1×rec-exp diff-log 1-exp pow-prod-down associate-*l/ *-commutative
Counts
4 → 1133
Calls
4 calls:
71.0ms
(- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d)))
308.0ms
(* (/ 1 (hypot c d)) (- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d))))
18.0ms
(/ c (/ (hypot c d) b))
21.0ms
(/ (* a d) (hypot c d))

series721.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d)))
337.0ms
(* (/ 1 (hypot c d)) (- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d))))
105.0ms
(/ c (/ (hypot c d) b))
84.0ms
(/ (* a d) (hypot c d))

simplify2.0s

Counts
1145 → 1145
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0126271346
1304958049
done500047628

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ d (sqrt (hypot c d)))
0.3b
(/ d (sqrt (hypot c d)))
0.5b
(+ (- (/ a (sqrt (hypot c d)))) (/ a (sqrt (hypot c d))))
3.5b
(* (/ d (sqrt (hypot c d))) (/ a (sqrt (hypot c d))))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
236×times-frac
205×add-sqr-sqrt
187×*-un-lft-identity
151×add-cube-cbrt
124×sqrt-prod
63×distribute-lft-neg-in
50×distribute-rgt-neg-in
48×fma-def
41×distribute-rgt-out
29×distribute-lft-out
22×associate-*r* associate-*l*
20×add-exp-log add-cbrt-cube
12×associate-/r*
10×div-inv
9×unswap-sqr
8×add-log-exp
6×pow1 cbrt-undiv div-exp associate-/l*
5×neg-mul-1
4×expm1-log1p-u distribute-lft1-in prod-exp cbrt-unprod log1p-expm1-u
2×frac-2neg clear-num sum-log
1×+-commutative neg-sub0 frac-times associate-+l- flip3-+ associate-*r/ pow-prod-down neg-log associate-*l/ frac-add *-commutative flip-+ distribute-neg-frac
Counts
4 → 295
Calls
4 calls:
6.0ms
(/ d (sqrt (hypot c d)))
6.0ms
(/ d (sqrt (hypot c d)))
97.0ms
(+ (- (/ a (sqrt (hypot c d)))) (/ a (sqrt (hypot c d))))
42.0ms
(* (/ d (sqrt (hypot c d))) (/ a (sqrt (hypot c d))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ d (sqrt (hypot c d)))
103.0ms
(/ d (sqrt (hypot c d)))
3.0ms
(+ (- (/ a (sqrt (hypot c d)))) (/ a (sqrt (hypot c d))))
102.0ms
(* (/ d (sqrt (hypot c d))) (/ a (sqrt (hypot c d))))

simplify1.2s

Counts
307 → 307
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02914007
16973334
218582963
done50012122

prune998.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

0% (0.9b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 3 (7.0ms)

IterNodesCost
02358
13658
24458
34957
done4957

end0.0ms

sample862.0ms

Algorithm
intervals
Results
530.0ms8494×body80valid