Details

sample56.0ms

Algorithm

intervals

Results

40.0ms

267×

body

valid

simplify28.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

27.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize20.0ms

Local error

Found 3 expressions with local error:

23.6b	(/ (fma a c (* b d)) (fma d d (* c c)))
0.5b	(fma a c (* b d))
0.0b	(fma d d (* c c))

rewrite13.0ms

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`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

Calls

3 calls:

Slowest

12.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms	(fma a c (* b d))
0.0ms	(fma d d (* c c))

series187.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

101.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))
48.0ms	(fma a c (* b d))
37.0ms	(fma d d (* c c))

simplify1.5s

Counts

34 → 61

Calls

34 calls:

Slowest

494.0ms	(/ (* (* (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))))
312.0ms	(- (log (fma a c (* b d))) (log (fma d d (* c c))))
45.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
41.0ms	(/ (fma a c (* b d)) (cbrt (fma d d (* c c))))
37.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (fma d d (* c c))))

prune658.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 23.2b

localize22.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (fma d d (* c c)))
27.9b	(sqrt (fma d d (* c c)))
13.0b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.5b	(fma a c (* b d))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

9.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))
0.0ms	(fma a c (* b d))

series357.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
75.0ms	(sqrt (fma d d (* c c)))
70.0ms	(sqrt (fma d d (* c c)))
54.0ms	(fma a c (* b d))

simplify1.8s

Counts

68 → 99

Calls

68 calls:

Slowest

296.0ms	(/ (* (* (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)))))
60.0ms	(/ (* (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))))))
53.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c)))))
48.0ms	(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (sqrt (sqrt (fma d d (* c c)))))
47.0ms	(/ (* (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))))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.6b

localize38.0ms

Local error

Found 4 expressions with local error:

27.9b	(sqrt (fma d d (* c c)))
27.9b	(sqrt (fma d d (* c c)))
13.2b	(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
0.5b	(fma a c (* b d))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `fma-udef`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

Slowest

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

series331.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

138.0ms	(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
76.0ms	(sqrt (fma d d (* c c)))
61.0ms	(sqrt (fma d d (* c c)))
55.0ms	(fma a c (* b d))

simplify1.5s

Counts

68 → 99

Calls

68 calls:

Slowest

248.0ms	(/ (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))) (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))))
50.0ms	(/ (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))) (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))))
46.0ms	(- (log (sqrt (fma d d (* c c)))) (log (fma a c (* b d))))
39.0ms	(/ (sqrt (sqrt (fma d d (* c c)))) (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))))
37.0ms	(/ 1 (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))))

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.6b

localize38.0ms

Local error

Found 4 expressions with local error:

23.3b	(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
0.5b	(fma a c (* b d))
0.5b	(/ 1 (fma d d (* c c)))
0.0b	(fma d d (* c c))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 95

Calls

4 calls:

Slowest

9.0ms	(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
4.0ms	(/ 1 (fma d d (* c c)))
0.0ms	(fma a c (* b d))
0.0ms	(fma d d (* c c))

series260.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

98.0ms	(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
59.0ms	(/ 1 (fma d d (* c c)))
53.0ms	(fma d d (* c c))
50.0ms	(fma a c (* b d))

simplify2.4s

Counts

69 → 107

Calls

69 calls:

Slowest

498.0ms	(* (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (/ 1 (fma d d (* c c))) (/ 1 (fma d d (* c c)))) (/ 1 (fma d d (* c c)))))
155.0ms	(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
136.0ms	(* (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (/ (* (* 1 1) 1) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c)))))
122.0ms	(/ (* (* 1 1) 1) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
88.0ms	(+ (log (fma a c (* b d))) (- (log 1) (log (fma d d (* c c)))))

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 21.6b

regimes293.0ms

Accuracy

0% (2.6b remaining)

Error of 26.1b against oracle of 23.5b and baseline of 26.1b

bsearch1.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

945.0ms

8449×

body

valid