Details

Time bar (total: 19.1s)

sample51.0ms

Algorithm
intervals
Results
34.0ms271×body80valid

simplify21.0ms

Counts
1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize27.0ms

Local error

Found 2 expressions with local error:

23.4b
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0b
(fma d d (* c c))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
Slowest
8.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms
(fma d d (* c c))

series192.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
134.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
58.0ms
(fma d d (* c c))

simplify912.0ms

Counts
47 → 47

prune526.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.0b

localize45.0ms

Local error

Found 4 expressions with local error:

26.2b
(sqrt (fma d d (* c c)))
26.2b
(sqrt (fma d d (* c c)))
14.2b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.1b
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×associate-/l/
Counts
4 → 254
Calls
4 calls:
Slowest
20.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
9.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
3.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
135.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
78.0ms
(sqrt (fma d d (* c c)))
59.0ms
(sqrt (fma d d (* c c)))

simplify2.1s

Counts
266 → 266

prune3.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.3b

localize25.0ms

Local error

Found 4 expressions with local error:

26.2b
(sqrt (fma d d (* c c)))
26.2b
(sqrt (fma d d (* c c)))
14.2b
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
0.2b
(/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
98×add-sqr-sqrt
96×*-un-lft-identity add-cube-cbrt
54×sqrt-prod
25×associate-/r*
17×add-exp-log
11×add-cbrt-cube
9×associate-/l*
8×div-exp
7×pow1
6×div-inv
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp fma-udef hypot-def
1×associate-/r/ pow-flip inv-pow
Counts
4 → 191
Calls
4 calls:
Slowest
13.0ms
(/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d))))
5.0ms
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
1.0ms
(sqrt (fma d d (* c c)))
1.0ms
(sqrt (fma d d (* c c)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d))))
95.0ms
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
52.0ms
(sqrt (fma d d (* c c)))
48.0ms
(sqrt (fma d d (* c c)))

simplify1.1s

Counts
203 → 203

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.0b

localize27.0ms

Local error

Found 4 expressions with local error:

26.2b
(sqrt (fma d d (* c c)))
14.2b
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
0.2b
(/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d))))
0.1b
(/ (/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d)))) (hypot d c))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
849×times-frac
416×add-sqr-sqrt
415×*-un-lft-identity add-cube-cbrt
159×sqrt-prod
80×associate-/l*
36×add-exp-log
28×associate-/r*
23×div-inv
22×div-exp
20×add-cbrt-cube
10×cbrt-undiv
6×pow1
5×associate-/r/
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef hypot-def pow-flip inv-pow associate-/l/
Counts
4 → 485
Calls
4 calls:
Slowest
17.0ms
(/ (/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d)))) (hypot d c))
8.0ms
(/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d))))
5.0ms
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
1.0ms
(sqrt (fma d d (* c c)))

series573.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
250.0ms
(/ (/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d)))) (hypot d c))
175.0ms
(/ 1 (/ (sqrt (fma d d (* c c))) (fma a c (* b d))))
99.0ms
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
48.0ms
(sqrt (fma d d (* c c)))

simplify771.0ms

Counts
497 → 497

prune5.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

regimes230.0ms

Accuracy

16.7% (9.6b remaining)

Error of 14.9b against oracle of 5.3b and baseline of 16.8b

bsearch47.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
753.0ms8474×body80valid