Details

Time bar (total: 13.1s)

sample22.0ms

Algorithm
intervals
Results
9.0ms269×body80valid

simplify66.0ms

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: 28.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(- (* b c) (* a d))
27.7b
(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite33.0ms

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:
12.0ms
(- (* b c) (* a d))
20.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

series139.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(- (* b c) (* a d))
97.0ms
(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.1s

Counts
54 → 54
Iterations

Useful iterations: done (2.1s)

IterNodesCost
087931
1214906
2710807
32547807
done5000801

prune168.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 17.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.2b
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
0.3b
(- (* b c) (* a d))
17.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite76.0ms

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:
6.0ms
(/ 1 (hypot c d))
34.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
11.0ms
(- (* b c) (* a d))
20.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series415.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ 1 (hypot c d))
187.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
42.0ms
(- (* b c) (* a d))
129.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify1.4s

Counts
151 → 151
Iterations

Useful iterations: 2 (239.0ms)

IterNodesCost
01772462
14682264
215591997
done50011997

prune330.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d)))
0.2b
(* (/ 1 (hypot c d)) (- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d))))
9.2b
(/ (* a d) (hypot c d))
9.3b
(/ c (/ (hypot c d) b))

rewrite405.0ms

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:
67.0ms
(- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d)))
198.0ms
(* (/ 1 (hypot c d)) (- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d))))
12.0ms
(/ (* a d) (hypot c d))
9.0ms
(/ c (/ (hypot c d) b))

series644.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d)))
300.0ms
(* (/ 1 (hypot c d)) (- (/ c (/ (hypot c d) b)) (/ (* a d) (hypot c d))))
72.0ms
(/ (* a d) (hypot c d))
98.0ms
(/ c (/ (hypot c d) b))

simplify1.9s

Counts
1145 → 1145
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0126271346
1304958049
done500047624

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
0.6b
(cbrt c)
2.5b
(* (/ d (hypot c d)) (- a))
3.7b
(/ (cbrt c) (/ (sqrt (hypot c d)) b))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
268×times-frac
158×add-sqr-sqrt
153×add-cube-cbrt *-un-lft-identity
75×cbrt-prod
63×sqrt-prod
22×associate-/r*
14×add-exp-log
13×associate-*l*
12×add-cbrt-cube
10×associate-*r*
9×div-inv
6×pow1 associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×distribute-lft-neg-in distribute-rgt-neg-in
2×pow1/3 prod-exp cbrt-unprod unswap-sqr
1×neg-mul-1 frac-2neg pow-prod-down associate-*l/ clear-num associate-/r/ *-commutative distribute-rgt-neg-out
Counts
4 → 245
Calls
4 calls:
1.0ms
(cbrt c)
1.0ms
(cbrt c)
19.0ms
(* (/ d (hypot c d)) (- a))
13.0ms
(/ (cbrt c) (/ (sqrt (hypot c d)) b))

series723.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt c)
186.0ms
(cbrt c)
94.0ms
(* (/ d (hypot c d)) (- a))
268.0ms
(/ (cbrt c) (/ (sqrt (hypot c d)) b))

simplify1.2s

Counts
257 → 257
Iterations

Useful iterations: done (1.2s)

IterNodesCost
04234451
19744049
230733865
done50003853

prune893.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.9b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02047
12647
23047
33347
done3347

end0.0ms

sample554.0ms

Algorithm
intervals
Results
268.0ms8473×body80valid