Details

sample75.0ms

Algorithm

intervals

Results

18.0ms	201×	body	80	valid
16.0ms	31×	body	2560	valid
10.0ms	23×	body	1280	valid
9.0ms	108×	body	80	nan
4.0ms	11×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	3×	body	160	valid

simplify160.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

159.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize42.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (- (* b b) (* (* 3 a) c)))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b	(* (* 3 a) c)
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
10×	`pow1` `fma-def`
8×	`add-log-exp`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `neg-mul-1` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `associate-l` `neg-log` `-commutative` `div-inv` `flip--`

Counts

4 → 98

Calls

4 calls:

Slowest

48.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
25.0ms	(* (* 3 a) c)
19.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
17.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

148.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
127.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
91.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
22.0ms	(* (* 3 a) c)

simplify5.4s

Counts

57 → 110

Calls

57 calls:

Slowest

666.0ms	(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
483.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
434.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
334.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
322.0ms	(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.7b

localize45.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (fma -3 (* c a) (* b b)))
1.0b	(- (sqrt (fma -3 (* c a) (* b b))) b)
0.3b	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
0.1b	(fma -3 (* c a) (* b b))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
30×	`add-cube-cbrt`
22×	`associate-r`
19×	`times-frac` `sqrt-prod`
18×	`prod-diff`
9×	`add-cbrt-cube` `add-exp-log`
8×	`difference-of-squares`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv` `flip--`

Counts

4 → 113

Calls

4 calls:

Slowest

38.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
11.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
3.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))

series412.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

135.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
100.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
97.0ms	(sqrt (fma -3 (* c a) (* b b)))
80.0ms	(fma -3 (* c a) (* b b))

simplify4.1s

Counts

97 → 125

Calls

97 calls:

Slowest

212.0ms	(* (* (* 1/3 1/3) 1/3) (/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* a a) a)))
154.0ms	(* (* (* 1/3 1/3) 1/3) (* (* (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a) (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)) (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)))
142.0ms	(+ (log 1/3) (log (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)))
142.0ms	(+ (log 1/3) (- (log (- (sqrt (fma -3 (* c a) (* b b))) b)) (log a)))
141.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.6b

localize41.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))
13.2b	(cbrt (* (* 3 a) c))
13.2b	(cbrt (* (* 3 a) c))
13.2b	(cbrt (* (* 3 a) c))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 54

Calls

4 calls:

Slowest

19.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))
11.0ms	(cbrt (* (* 3 a) c))
10.0ms	(cbrt (* (* 3 a) c))
10.0ms	(cbrt (* (* 3 a) c))

series595.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

177.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))
150.0ms	(cbrt (* (* 3 a) c))
147.0ms	(cbrt (* (* 3 a) c))
120.0ms	(cbrt (* (* 3 a) c))

simplify4.9s

Counts

22 → 66

Calls

22 calls:

Slowest

602.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c))) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c))))))
407.0ms	(* (exp (* -1/3 (+ (log (/ -1 c)) (log (/ -1 a))))) (cbrt 3))
401.0ms	(* (cbrt 3) (exp (* 1/3 (+ (log a) (log c)))))
386.0ms	(* (cbrt 3) (exp (* 1/3 (+ (log a) (log c)))))
381.0ms	(* (exp (* -1/3 (+ (log (/ -1 c)) (log (/ -1 a))))) (cbrt 3))

prune941.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.6b

localize46.0ms

Local error

Found 4 expressions with local error:

17.4b	(sqrt (fma -3 (* c a) (* b b)))
1.0b	(- (sqrt (fma -3 (* c a) (* b b))) b)
0.5b	(cbrt a)
0.5b	(cbrt a)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
6×	`cbrt-prod` `fma-neg` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`pow1/3` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

Slowest

13.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
1.0ms	(sqrt (fma -3 (* c a) (* b b)))
1.0ms	(cbrt a)
1.0ms	(cbrt a)

series818.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

300.0ms	(cbrt a)
296.0ms	(cbrt a)
112.0ms	(sqrt (fma -3 (* c a) (* b b)))
109.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.1s

Counts

70 → 98

Calls

70 calls:

Slowest

120.0ms	(* (pow (* a -1) 1/3) (cbrt -1))
107.0ms	(fma (* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b))))) (cbrt (sqrt (fma -3 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
98.0ms	(* (pow (* a -1) 1/3) (cbrt -1))
88.0ms	(fma (* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b))))) (cbrt (sqrt (fma -3 (* c a) (* b b)))) (- (* b 1)))
75.0ms	(fma (* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b))))) (cbrt (sqrt (fma -3 (* c a) (* b b)))) (- (* (sqrt b) (sqrt b))))

prune1.3s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 4.6b

regimes792.0ms

Accuracy

83.3% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.4b

bsearch165.0ms

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.1s	899×	body	1280	valid
998.0ms	1068×	body	2560	valid
895.0ms	5900×	body	80	valid
699.0ms	446×	body	640	valid
393.0ms	2909×	body	80	nan
149.0ms	272×	body	320	valid
95.0ms	108×	body	5120	valid
24.0ms	104×	body	160	valid