Details

sample35.0ms

Algorithm

intervals

Results

25.0ms

270×

body

valid

simplify145.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

145.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize22.0ms

Local error

Found 2 expressions with local error:

25.2b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.2b	(- (* b c) (* a d))

rewrite56.0ms

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` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

2 → 50

Calls

2 calls:

Slowest

39.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
16.0ms	(- (* b c) (* a d))

series178.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

123.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
56.0ms	(- (* b c) (* a d))

simplify2.5s

Counts

37 → 56

Calls

37 calls:

Slowest

563.0ms	(/ (* (* (- (* 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))))
381.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
257.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
148.0ms	(/ (exp (* b c)) (exp (* a d)))
118.0ms	(/ (- (* b c) (* a d)) (cbrt (fma d d (* c c))))

prune694.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.8b

localize37.0ms

Local error

Found 4 expressions with local error:

30.1b	(sqrt (fma d d (* c c)))
30.1b	(sqrt (fma d d (* c c)))
14.9b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.2b	(- (* b c) (* a d))

rewrite42.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 96

Calls

4 calls:

Slowest

22.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
16.0ms	(- (* b c) (* a d))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
61.0ms	(sqrt (fma d d (* c c)))
60.0ms	(sqrt (fma d d (* c c)))
56.0ms	(- (* b c) (* a d))

simplify3.9s

Counts

74 → 108

Calls

74 calls:

Slowest

489.0ms	(/ (- (* b c) (* a d)) (sqrt (cbrt (fma d d (* c c)))))
453.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
397.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
247.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
165.0ms	(/ (exp (* b c)) (exp (* a d)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.0b

localize53.0ms

Local error

Found 4 expressions with local error:

30.1b	(sqrt (fma d d (* c c)))
14.9b	(/ (- (* b c) (* a d)) (hypot d c))
0.2b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 183

Calls

4 calls:

Slowest

39.0ms	(/ (- (* b c) (* a d)) (hypot d c))
29.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
16.0ms	(- (* b c) (* a d))
3.0ms	(sqrt (fma d d (* c c)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

235.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
175.0ms	(/ (- (* b c) (* a d)) (hypot d c))
63.0ms	(sqrt (fma d d (* c c)))
52.0ms	(- (* b c) (* a d))

simplify18.4s

Counts

228 → 195

Calls

228 calls:

Slowest

469.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
356.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
334.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
317.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (sqrt (fma d d (* c c)))))
283.0ms	(/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.3b

localize31.0ms

Local error

Found 4 expressions with local error:

14.9b	(/ (- (* b c) (* a d)) (hypot d c))
0.2b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
0.0b	(hypot d c)

rewrite44.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`hypot-udef` `sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 135

Calls

4 calls:

Slowest

17.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
16.0ms	(/ (- (* b c) (* a d)) (hypot d c))
9.0ms	(- (* b c) (* a d))
0.0ms	(hypot d c)

series395.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(/ (- (* b c) (* a d)) (hypot d c))
136.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
65.0ms	(hypot d c)
43.0ms	(- (* b c) (* a d))

simplify8.2s

Counts

142 → 147

Calls

142 calls:

Slowest

378.0ms	(/ (/ (- (* b c) (* a d)) (cbrt (hypot d c))) (cbrt (hypot d c)))
361.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
351.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
222.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
164.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (hypot d c)))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

regimes264.0ms

Accuracy

16% (8.8b remaining)

Error of 15.0b against oracle of 6.2b and baseline of 16.6b

bsearch44.0ms

end0.0ms

sample1.0s

Algorithm

intervals

Results

854.0ms

8462×

body

valid