Details

sample45.0ms

Algorithm

intervals

Results

34.0ms

272×

body

valid

simplify93.0ms

Calls

1 calls:

Slowest

92.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize17.0ms

Local error

Found 2 expressions with local error:

24.9b	(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.7b	(- (* b c) (* a d))

rewrite10.0ms

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`

Calls

2 calls:

Slowest

7.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
2.0ms	(- (* b c) (* a d))

series109.0ms

Calls

2 calls:

Slowest

75.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))
34.0ms	(- (* b c) (* a d))

simplify1.9s

Calls

37 calls:

Slowest

413.0ms	(/ (* (* (- (* 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))))
267.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
211.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
91.0ms	(/ (- (* b c) (* a d)) (cbrt (fma d d (* c c))))
76.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

prune586.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.5b

localize8.0ms

Local error

Found 4 expressions with local error:

28.1b	(sqrt (fma d d (* c c)))
28.1b	(sqrt (fma d d (* c c)))
15.7b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.7b	(- (* b c) (* a d))

rewrite18.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `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`

Calls

4 calls:

Slowest

10.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
4.0ms	(- (* b c) (* a d))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series179.0ms

Calls

4 calls:

Slowest

87.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
34.0ms	(sqrt (fma d d (* c c)))
31.0ms	(sqrt (fma d d (* c c)))
27.0ms	(- (* b c) (* a d))

simplify2.9s

Calls

72 calls:

Slowest

379.0ms	(/ (* (* (- (* 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)))))
340.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
236.0ms	(- (* (* b c) (* b c)) (* (* a d) (* a d)))
119.0ms	(/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c)))))
112.0ms	(/ (- (* b c) (* a d)) (sqrt (cbrt (fma d d (* c c)))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.4b

localize6.0ms

Local error

Found 4 expressions with local error:

28.1b	(sqrt (fma d d (* c c)))
15.7b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.7b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a 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` `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×	`rem-sqrt-square` `sub-neg` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Calls

4 calls:

Slowest

12.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
8.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(- (* b c) (* a d))
1.0ms	(sqrt (fma d d (* c c)))

series233.0ms

Calls

4 calls:

Slowest

109.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
76.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
27.0ms	(- (* b c) (* a d))
22.0ms	(sqrt (fma d d (* c c)))

simplify12.9s

Calls

230 calls:

Slowest

373.0ms	(/ (* (* (- (* 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)))))
295.0ms	(/ (/ (cbrt (- (* b c) (* a d))) (sqrt (fma d d (* c c)))) (cbrt (hypot d c)))
235.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
178.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c))))) (hypot d c))
175.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c))))) (hypot d c))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize5.0ms

Local error

Found 3 expressions with local error:

15.7b	(/ (- (* b c) (* a d)) (hypot d c))
0.7b	(- (* b c) (* a d))
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))

rewrite20.0ms

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`

Calls

3 calls:

Slowest

10.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
7.0ms	(/ (- (* b c) (* a d)) (hypot d c))
2.0ms	(- (* b c) (* a d))

series165.0ms

Calls

3 calls:

Slowest

69.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
68.0ms	(/ (- (* b c) (* a d)) (hypot d c))
27.0ms	(- (* b c) (* a d))

simplify6.2s

Calls

139 calls:

Slowest

219.0ms	(- (pow (* b c) 3) (pow (* a d) 3))
214.0ms	(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (hypot d c) (hypot d c)) (hypot d c)))
149.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (hypot d c)))
148.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (cbrt (hypot d c)))
148.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (hypot d c)))

prune838.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

regimes186.0ms

Accuracy

36.2% (7.0b remaining)

Error of 12.7b against oracle of 5.7b and baseline of 16.7b

bsearch86.0ms

end0.0ms

sample950.0ms

Algorithm

intervals

Results

750.0ms

8498×

body

valid