Details

sample40.0ms

Algorithm

intervals

Results

30.0ms

274×

body

valid

simplify21.0ms

Calls

1 calls:

Slowest

21.0ms

(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize26.0ms

Local error

Found 2 expressions with local error:

23.3b	(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b	(fma a c (* b d))

rewrite7.0ms

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`

Calls

2 calls:

Slowest

6.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series193.0ms

Calls

2 calls:

Slowest

130.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
63.0ms	(fma a c (* b d))

simplify917.0ms

Calls

31 calls:

Slowest

304.0ms	(/ (* (* (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))))
70.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
34.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (fma d d (* c c))))
32.0ms	(/ (sqrt (fma a c (* b d))) (sqrt (fma d d (* c c))))
30.0ms	(/ (fma a c (* b d)) (cbrt (fma d d (* c c))))

prune550.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.9b

localize13.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (fma d d (* c c)))
27.8b	(sqrt (fma d d (* c c)))
14.5b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b	(fma a c (* b 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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Calls

4 calls:

Slowest

7.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series282.0ms

Calls

4 calls:

Slowest

122.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
63.0ms	(sqrt (fma d d (* c c)))
52.0ms	(sqrt (fma d d (* c c)))
45.0ms	(fma a c (* b d))

simplify1.6s

Calls

66 calls:

Slowest

277.0ms	(/ (* (* (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)))))
51.0ms	(/ (* (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))))))
48.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt 1))
41.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) 1)
41.0ms	(- (log (fma a c (* b d))) (log (sqrt (fma d d (* c c)))))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.2b

localize6.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (fma d d (* c c)))
14.5b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`rem-sqrt-square` `pow1/2` `hypot-def` `associate-/l/`

Calls

4 calls:

Slowest

15.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
5.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series438.0ms

Calls

4 calls:

Slowest

192.0ms	(/ (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (hypot d c))
132.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
57.0ms	(fma a c (* b d))
56.0ms	(sqrt (fma d d (* c c)))

simplify7.7s

Calls

223 calls:

Slowest

304.0ms	(/ (/ (cbrt (fma a c (* b d))) (sqrt (sqrt (fma d d (* c c))))) (sqrt (hypot d c)))
272.0ms	(/ (* (* (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)))))
182.0ms	(/ (/ (* (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 (hypot d c)) (cbrt (hypot d c))))
163.0ms	(/ (* (* (/ (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))))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
135.0ms	(/ (/ (* (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 (hypot d c)) (cbrt (hypot d c))))

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize6.0ms

Local error

Found 4 expressions with local error:

14.5b	(/ (fma a c (* b d)) (hypot d c))
0.3b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
0.0b	(hypot d c)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Calls

4 calls:

Slowest

8.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
4.0ms	(/ (fma a c (* b d)) (hypot d c))
0.0ms	(hypot d c)
0.0ms	(fma a c (* b d))

series325.0ms

Calls

4 calls:

Slowest

119.0ms	(/ (fma a c (* b d)) (hypot d c))
116.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
49.0ms	(hypot d c)
40.0ms	(fma a c (* b d))

simplify3.3s

Calls

135 calls:

Slowest

282.0ms	(/ (* (* (/ (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)))
181.0ms	(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
109.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (sqrt (hypot d c)))
107.0ms	(/ (/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (hypot d c))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))
101.0ms	(/ (/ (* (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))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

regimes275.0ms

Accuracy

18.3% (8.6b remaining)

Error of 14.6b against oracle of 6.0b and baseline of 16.5b

bsearch31.0ms

end0.0ms

sample977.0ms

Algorithm

intervals

Results

784.0ms

8451×

body

valid