Details

Time bar (total: 1.2m)

sample41.0ms

Algorithm
intervals
Results
28.0ms274×body80valid

simplify20.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
19.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize30.0ms

Local error

Found 2 expressions with local error:

25.6b
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0b
(fma a c (* b d))

rewrite5.0ms

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
4.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series180.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
125.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
55.0ms
(fma a c (* b d))

simplify1.1s

Counts
31 → 47
Calls
31 calls:
Slowest
393.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
58.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
39.0ms
(- (log (fma a c (* b d))) (log (fma d d (* c c))))
38.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
38.0ms
(/ 1 (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))

prune625.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.1b

localize44.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (fma d d (* c c)))
29.7b
(sqrt (fma d d (* c c)))
16.1b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.0b
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))

rewrite26.0ms

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
9.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
8.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
2.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
130.0ms
(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
63.0ms
(sqrt (fma d d (* c c)))
59.0ms
(sqrt (fma d d (* c c)))

simplify16.3s

Counts
364 → 266
Calls
364 calls:
Slowest
481.0ms
(/ (* (* (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
288.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
220.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c)))))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))
211.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c)))))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))
203.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.5b

localize19.0ms

Local error

Found 3 expressions with local error:

16.1b
(/ (fma a c (* b d)) (hypot d c))
0.0b
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.0b
(fma a c (* b d))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
10×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×fma-udef associate-/l/
Counts
3 → 114
Calls
3 calls:
Slowest
7.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
5.0ms
(/ (fma a c (* b d)) (hypot d c))
0.0ms
(fma a c (* b d))

series375.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
175.0ms
(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
135.0ms
(/ (fma a c (* b d)) (hypot d c))
65.0ms
(fma a c (* b d))

simplify4.6s

Counts
132 → 123
Calls
132 calls:
Slowest
362.0ms
(/ (* (* (/ (fma a c (* b d)) (hypot d c)) (/ (fma a c (* b d)) (hypot d c))) (/ (fma a c (* b d)) (hypot d c))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
258.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
156.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
126.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (hypot d c)))
126.0ms
(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (hypot d c))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.9b

localize32.0ms

Local error

Found 4 expressions with local error:

16.1b
(/ (hypot d c) (fma a c (* b d)))
0.2b
(/ 1 (/ (hypot d c) (fma a c (* b d))))
0.0b
(/ (/ 1 (/ (hypot d c) (fma a c (* b d)))) (hypot d c))
0.0b
(fma a c (* b d))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 323
Calls
4 calls:
Slowest
11.0ms
(/ (/ 1 (/ (hypot d c) (fma a c (* b d)))) (hypot d c))
11.0ms
(/ 1 (/ (hypot d c) (fma a c (* b d))))
8.0ms
(/ (hypot d c) (fma a c (* b d)))
0.0ms
(fma a c (* b d))

series563.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(/ (/ 1 (/ (hypot d c) (fma a c (* b d)))) (hypot d c))
170.0ms
(/ 1 (/ (hypot d c) (fma a c (* b d))))
126.0ms
(/ (hypot d c) (fma a c (* b d)))
47.0ms
(fma a c (* b d))

simplify40.9s

Counts
457 → 335
Calls
457 calls:
Slowest
598.0ms
(/ (* (* 1 1) 1) (/ (* (* (hypot d c) (hypot d c)) (hypot d c)) (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d)))))
499.0ms
(/ (/ 1 (/ (cbrt (hypot d c)) (fma a c (* b d)))) (hypot d c))
487.0ms
(/ (/ (* (* 1 1) 1) (* (* (/ (hypot d c) (fma a c (* b d))) (/ (hypot d c) (fma a c (* b d)))) (/ (hypot d c) (fma a c (* b d))))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
468.0ms
(/ (sqrt 1) (/ (* (cbrt (hypot d c)) (cbrt (hypot d c))) (sqrt (fma a c (* b d)))))
437.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (hypot d c)) (cbrt (hypot d c))) (sqrt (fma a c (* b d))))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))

prune2.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.5b

regimes243.0ms

Accuracy

25% (10.8b remaining)

Error of 13.1b against oracle of 2.3b and baseline of 16.7b

bsearch82.0ms

end0.0ms

sample905.0ms

Algorithm
intervals
Results
742.0ms8459×body80valid