Details

sample145.0ms

Algorithm

intervals

Results

37.0ms	146×	body	160	valid
32.0ms	525×	pre	80	true
30.0ms	269×	body	80	nan
14.0ms	110×	body	80	valid

simplify145.0ms

Counts: 1 → 1

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.0b

localize42.0ms

Local error

Found 4 expressions with local error:

28.9b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.4b	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
0.2b	(fma c (* -3 a) (* b b))
0.1b	(sqrt (fma c (* -3 a) (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `fma-neg` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 102

Calls

4 calls:

Slowest

23.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
8.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -3 a) (* b b)))
0.0ms	(fma c (* -3 a) (* b b))

series393.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

117.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
114.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
96.0ms	(sqrt (fma c (* -3 a) (* b b)))
66.0ms	(fma c (* -3 a) (* b b))

simplify543.0ms

Counts: 145 → 114

prune1.4s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 26.2b

localize52.0ms

Local error

Found 4 expressions with local error:

27.4b	(- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b)))
0.4b	(/ (/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
0.4b	(/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
0.3b	(* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
48×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
12×	`pow3`
11×	`difference-cubes` `cube-unmult`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`flip3-+` `div-sub` `associate-l` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `pow-prod-up` `flip--` `unswap-sqr`
1×	`sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `*-commutative`

Counts

4 → 145

Calls

4 calls:

Slowest

74.0ms	(/ (/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
73.0ms	(/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
20.0ms	(- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b)))
7.0ms	(* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c))))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

535.0ms	(/ (/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
486.0ms	(/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
174.0ms	(- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b)))
114.0ms	(* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c))))

simplify631.0ms

Counts: 195 → 157

prune2.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 2.7b

localize102.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (- (/ (* 27/8 (* (* a a) (* c c))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
0.4b	(/ (- (/ (* 27/8 (* (* a a) (* c c))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
0.3b	(* (* a a) (* c c))
0.3b	(* (* 9/2 a) (* c b))

rewrite462.0ms

Algorithm

rewrite-expression-head

Rules

44×	`pow1`
42×	`times-frac` `add-cbrt-cube` `add-exp-log`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
22×	`pow-prod-down`
18×	`prod-exp` `cbrt-unprod` `associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
4×	`expm1-log1p-u` `associate-/r*` `pow-plus` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `div-sub` `flip-+` `associate-/l/`
2×	`pow2` `clear-num` `frac-2neg` `associate-r` `associate-l` `pow-sqr` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

Slowest

212.0ms	(/ (/ (- (/ (* 27/8 (* (* a a) (* c c))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
195.0ms	(/ (- (/ (* 27/8 (* (* a a) (* c c))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
29.0ms	(* (* a a) (* c c))
24.0ms	(* (* 9/2 a) (* c b))

series545.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

277.0ms	(/ (/ (- (/ (* 27/8 (* (* a a) (* c c))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
190.0ms	(/ (- (/ (* 27/8 (* (* a a) (* c c))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
40.0ms	(* (* a a) (* c c))
38.0ms	(* (* 9/2 a) (* c b))

simplify474.0ms

Counts: 185 → 158

prune2.9s

Pruning

42 alts after pruning (42 fresh and 0 done)

Merged error: 2.3b

localize77.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* c a) (* c a))
0.4b	(/ (/ (- (/ (* 27/8 (* (* c a) (* c a))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
0.4b	(/ (- (/ (* 27/8 (* (* c a) (* c a))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
0.3b	(* (* 9/2 a) (* c b))

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

55×	`pow1`
42×	`times-frac` `add-cbrt-cube` `add-exp-log`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
25×	`pow-prod-down`
18×	`prod-exp` `cbrt-unprod` `associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
4×	`expm1-log1p-u` `associate-/r*` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `div-sub` `flip-+` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-plus` `associate-r` `associate-l` `*-commutative`
1×	`pow2` `flip3--` `swap-sqr` `flip--`

Counts

4 → 151

Calls

4 calls:

Slowest

251.0ms	(/ (/ (- (/ (* 27/8 (* (* c a) (* c a))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
233.0ms	(/ (- (/ (* 27/8 (* (* c a) (* c a))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
46.0ms	(* (* 9/2 a) (* c b))
33.0ms	(* (* c a) (* c a))

series523.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

231.0ms	(/ (/ (- (/ (* 27/8 (* (* c a) (* c a))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
221.0ms	(/ (- (/ (* 27/8 (* (* c a) (* c a))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c))))
36.0ms	(* (* c a) (* c a))
36.0ms	(* (* 9/2 a) (* c b))

simplify532.0ms

Counts: 189 → 163

prune2.9s

Pruning

42 alts after pruning (41 fresh and 1 done)

Merged error: 2.3b

regimes1.7s

Accuracy

23.1% (6.8b remaining)

Error of 9.2b against oracle of 2.4b and baseline of 11.2b

bsearch38.0ms

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.2s	4515×	body	160	valid
1.2s	16512×	pre	80	true
1.2s	8512×	body	80	nan
849.0ms	3485×	body	80	valid