Details

Time bar (total: 41.0s)

sample55.0ms

Algorithm
intervals
Results
42.0ms269×body80valid

simplify121.0ms

Calls
1 calls:
Slowest
120.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize17.0ms

Local error

Found 3 expressions with local error:

24.0b
(/ (- (* b c) (* a d)) (fma d d (* c c)))
1.2b
(- (* b c) (* a d))
0.0b
(fma d d (* c c))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log add-log-exp
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff fma-udef div-inv
Calls
3 calls:
Slowest
9.0ms
(/ (- (* b c) (* a d)) (fma d d (* c c)))
2.0ms
(- (* b c) (* a d))
0.0ms
(fma d d (* c c))

series118.0ms

Calls
3 calls:
Slowest
64.0ms
(/ (- (* b c) (* a d)) (fma d d (* c c)))
36.0ms
(- (* b c) (* a d))
18.0ms
(fma d d (* c c))

simplify2.0s

Calls
40 calls:
Slowest
445.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
326.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
193.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
114.0ms
(/ (- (* b c) (* a d)) (cbrt (fma d d (* c c))))
100.0ms
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))

prune732.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.6b

localize8.0ms

Local error

Found 4 expressions with local error:

23.9b
(/ (fma d d (* c c)) (- (* b c) (* a d)))
1.2b
(- (* b c) (* a d))
0.3b
(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
0.0b
(fma d d (* c c))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/r* times-frac
9×add-exp-log
6×add-cbrt-cube add-log-exp
5×pow1 associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-- div-inv flip-- associate-/l*
2×rec-exp clear-num frac-2neg div-exp
1×cbrt-undiv sub-neg fma-neg diff-log prod-diff fma-udef pow-flip inv-pow
Calls
4 calls:
Slowest
9.0ms
(/ (fma d d (* c c)) (- (* b c) (* a d)))
4.0ms
(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
4.0ms
(- (* b c) (* a d))
0.0ms
(fma d d (* c c))

series227.0ms

Calls
4 calls:
Slowest
105.0ms
(/ 1 (/ (fma d d (* c c)) (- (* b c) (* a d))))
63.0ms
(/ (fma d d (* c c)) (- (* b c) (* a d)))
41.0ms
(- (* b c) (* a d))
19.0ms
(fma d d (* c c))

simplify2.1s

Calls
59 calls:
Slowest
345.0ms
(/ (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))) (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))))
287.0ms
(+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d))))
241.0ms
(+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d))))
55.0ms
(/ (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))))
48.0ms
(/ 1 (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))))

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.6b

localize21.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (fma d d (* c c)))
29.0b
(sqrt (fma d d (* c c)))
16.2b
(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
1.2b
(- (* b c) (* a d))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×add-cbrt-cube add-exp-log associate-/l* add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×associate-/r*
2×rem-sqrt-square flip3-- pow1/2 associate-/r/ fma-udef hypot-def flip--
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-exp prod-diff div-inv
Calls
4 calls:
Slowest
6.0ms
(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
2.0ms
(- (* b c) (* a d))
1.0ms
(sqrt (fma d d (* c c)))
1.0ms
(sqrt (fma d d (* c c)))

series134.0ms

Calls
4 calls:
Slowest
55.0ms
(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
27.0ms
(- (* b c) (* a d))
27.0ms
(sqrt (fma d d (* c c)))
25.0ms
(sqrt (fma d d (* c c)))

simplify1.9s

Calls
71 calls:
Slowest
222.0ms
(/ (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))) (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))))
220.0ms
(+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d))))
55.0ms
(/ (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))))
49.0ms
(/ (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))) (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))))
42.0ms
(/ (exp (* b c)) (exp (* a d)))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.6b

localize11.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (fma d d (* c c)))
16.2b
(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
1.2b
(- (* b c) (* a d))
0.2b
(/ (/ 1 (/ (hypot d c) 1)) (/ (sqrt (fma d d (* c c))) (- (* b c) (* a d))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
246×times-frac
124×add-sqr-sqrt
123×*-un-lft-identity add-cube-cbrt
69×sqrt-prod
40×associate-/r/
33×div-inv
27×associate-/r*
16×add-exp-log
11×add-cbrt-cube associate-/l*
8×flip3-- flip--
7×div-exp
6×add-log-exp
4×expm1-log1p-u pow1 cbrt-undiv insert-posit16 log1p-expm1-u
2×rec-exp clear-num frac-2neg
1×rem-sqrt-square sub-neg pow1/2 fma-neg diff-log prod-diff fma-udef hypot-def associate-/l/
Calls
4 calls:
Slowest
10.0ms
(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
8.0ms
(/ (/ 1 (/ (hypot d c) 1)) (/ (sqrt (fma d d (* c c))) (- (* b c) (* a d))))
2.0ms
(- (* b c) (* a d))
1.0ms
(sqrt (fma d d (* c c)))

series284.0ms

Calls
4 calls:
Slowest
163.0ms
(/ (/ 1 (/ (hypot d c) 1)) (/ (sqrt (fma d d (* c c))) (- (* b c) (* a d))))
61.0ms
(/ (sqrt (fma d d (* c c))) (- (* b c) (* a d)))
37.0ms
(- (* b c) (* a d))
22.0ms
(sqrt (fma d d (* c c)))

simplify27.1s

Calls
341 calls:
Slowest
414.0ms
(/ (sqrt (/ 1 (/ (hypot d c) 1))) (/ 1 (- (* b c) (* a d))))
391.0ms
(/ (* (cbrt (/ 1 (/ (hypot d c) 1))) (cbrt (/ 1 (/ (hypot d c) 1)))) (/ (sqrt (fma d d (* c c))) (- (* (* b c) (* b c)) (* (* a d) (* a d)))))
335.0ms
(/ (* (cbrt (/ 1 (/ (hypot d c) 1))) (cbrt (/ 1 (/ (hypot d c) 1)))) (/ (sqrt (fma d d (* c c))) (- (pow (* b c) 3) (pow (* a d) 3))))
276.0ms
(/ (/ 1 (/ (hypot d c) 1)) (/ (sqrt (cbrt (fma d d (* c c)))) (- (* b c) (* a d))))
270.0ms
(/ (/ 1 (/ (hypot d c) 1)) (/ (sqrt (cbrt (fma d d (* c c)))) (- (* b c) (* a d))))

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.3b

regimes258.0ms

Accuracy

0% (0.4b remaining)

Error of 16.8b against oracle of 16.4b and baseline of 16.8b

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm
intervals
Results
934.0ms8503×body80valid