Details

sample66.0ms

Algorithm

intervals

Results

52.0ms

269×

body

valid

simplify110.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

109.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize18.0ms

Local error

Found 3 expressions with local error:

25.7b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.5b	(- (* b c) (* a d))
0.0b	(fma d d (* c c))

rewrite25.0ms

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`

Counts

3 → 61

Calls

3 calls:

Slowest

16.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
8.0ms	(- (* b c) (* a d))
0.0ms	(fma d d (* c c))

series240.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

141.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
56.0ms	(- (* b c) (* a d))
43.0ms	(fma d d (* c c))

simplify2.6s

Counts

40 → 70

Calls

40 calls:

Slowest

530.0ms	(/ (* (* (- (* 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))))
400.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
279.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
141.0ms	(/ (exp (* b c)) (exp (* a d)))
139.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

prune935.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.3b

localize56.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (fma d d (* c c)))
29.1b	(sqrt (fma d d (* c c)))
13.6b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.5b	(- (* b c) (* a d))

rewrite43.0ms

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

29.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
8.0ms	(- (* b c) (* a d))
3.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

181.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
81.0ms	(sqrt (fma d d (* c c)))
56.0ms	(- (* b c) (* a d))
47.0ms	(sqrt (fma d d (* c c)))

simplify3.5s

Counts

74 → 108

Calls

74 calls:

Slowest

414.0ms	(/ (* (* (- (* 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)))))
406.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
272.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
196.0ms	(/ (exp (* b c)) (exp (* a d)))
124.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.4b

localize28.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (fma d d (* c c)))
13.6b	(/ (- (* b c) (* a d)) (hypot d c))
0.5b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))

rewrite46.0ms

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

16.0ms	(/ (- (* b c) (* a d)) (hypot d c))
14.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
12.0ms	(- (* b c) (* a d))
1.0ms	(sqrt (fma d d (* c c)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

210.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
179.0ms	(/ (- (* b c) (* a d)) (hypot d c))
64.0ms	(sqrt (fma d d (* c c)))
64.0ms	(- (* b c) (* a d))

simplify19.2s

Counts

228 → 195

Calls

228 calls:

Slowest

514.0ms	(/ (sqrt (/ (- (* b c) (* a d)) (hypot d c))) 1)
473.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
444.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
393.0ms	(/ (/ (* (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))))))
314.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (sqrt (fma d d (* c c)))))

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize28.0ms

Local error

Found 3 expressions with local error:

13.6b	(/ (- (* b c) (* a d)) (hypot d c))
0.5b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))

rewrite52.0ms

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

Counts

3 → 124

Calls

3 calls:

Slowest

21.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
20.0ms	(/ (- (* b c) (* a d)) (hypot d c))
8.0ms	(- (* b c) (* a d))

series350.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

151.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
149.0ms	(/ (- (* b c) (* a d)) (hypot d c))
50.0ms	(- (* b c) (* a d))

simplify8.8s

Counts

139 → 133

Calls

139 calls:

Slowest

341.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
287.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
218.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (cbrt (hypot d c)))
215.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (hypot d c))) (cbrt (hypot d c)))
209.0ms	(/ (/ (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (* (cbrt (hypot d c)) (cbrt (hypot d c)))) (* (cbrt (hypot d c)) (cbrt (hypot d c))))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

regimes385.0ms

Accuracy

31.9% (6.9b remaining)

Error of 12.6b against oracle of 5.7b and baseline of 15.8b

bsearch129.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.4s

8461×

body

valid