Details

sample52.0ms

Algorithm

intervals

Results

37.0ms

272×

body

valid

simplify112.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

112.0ms

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize34.0ms

Local error

Found 2 expressions with local error:

24.2b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.7b	(- (* b c) (* a d))

rewrite34.0ms

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

26.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
8.0ms	(- (* b c) (* a d))

series210.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

144.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
67.0ms	(- (* b c) (* a d))

simplify2.1s

Counts

37 → 56

Calls

37 calls:

Slowest

471.0ms	(/ (* (* (- (* 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))))
343.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
197.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
154.0ms	(/ (exp (* b c)) (exp (* a d)))
97.0ms	(/ (- (* b c) (* a d)) (cbrt (fma d d (* c c))))

prune561.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.8b

localize43.0ms

Local error

Found 4 expressions with local error:

26.9b	(sqrt (fma d d (* c c)))
26.9b	(sqrt (fma d d (* c c)))
16.3b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.7b	(- (* b c) (* a d))

rewrite51.0ms

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

31.0ms	(/ (- (* 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)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

142.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
72.0ms	(sqrt (fma d d (* c c)))
54.0ms	(- (* b c) (* a d))
50.0ms	(sqrt (fma d d (* c c)))

simplify2.9s

Counts

74 → 108

Calls

74 calls:

Slowest

372.0ms	(/ (* (* (- (* 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)))))
303.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
195.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
146.0ms	(/ (exp (* b c)) (exp (* a d)))
114.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c)))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.6b

localize35.0ms

Local error

Found 4 expressions with local error:

26.9b	(sqrt (fma d d (* c c)))
26.9b	(sqrt (fma d d (* c c)))
16.3b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.7b	(- (* b c) (* a d))

rewrite28.0ms

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

16.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
8.0ms	(- (* b c) (* a d))
2.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
62.0ms	(sqrt (fma d d (* c c)))
47.0ms	(- (* b c) (* a d))
47.0ms	(sqrt (fma d d (* c c)))

simplify2.9s

Counts

74 → 108

Calls

74 calls:

Slowest

367.0ms	(/ (* (* (- (* 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)))))
326.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
192.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
166.0ms	(/ (exp (* b c)) (exp (* a d)))
121.0ms	(/ (- (* b c) (* a d)) (cbrt (sqrt (fma d d (* c c)))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.6b

localize26.0ms

Local error

Found 3 expressions with local error:

23.9b	(* (- (* b c) (* a d)) (/ 1 (fma d d (* c c))))
0.7b	(- (* b c) (* a d))
0.4b	(/ 1 (fma d d (* c c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `associate-/r` `flip3--` `associate-l` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 94

Calls

3 calls:

Slowest

37.0ms	(* (- (* b c) (* a d)) (/ 1 (fma d d (* c c))))
16.0ms	(- (* b c) (* a d))
8.0ms	(/ 1 (fma d d (* c c)))

series223.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

110.0ms	(* (- (* b c) (* a d)) (/ 1 (fma d d (* c c))))
65.0ms	(/ 1 (fma d d (* c c)))
47.0ms	(- (* b c) (* a d))

simplify3.9s

Counts

75 → 103

Calls

75 calls:

Slowest

704.0ms	(* (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (/ 1 (fma d d (* c c))) (/ 1 (fma d d (* c c)))) (/ 1 (fma d d (* c c)))))
348.0ms	(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) 1)
229.0ms	(* (- (* (* b c) (* b c)) (* (* a d) (* a d))) (/ 1 (fma d d (* c c))))
205.0ms	(* (+ (* b c) (* a d)) (fma d d (* c c)))
204.0ms	(* (- (* b c) (* a d)) (/ 1 (fma d d (* c c))))

prune791.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.6b

regimes246.0ms

Accuracy

0% (2.6b remaining)

Error of 25.7b against oracle of 23.1b and baseline of 25.7b

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8509×

body

valid