Details

sample148.0ms

Algorithm

intervals

Results

36.0ms	142×	body	160	valid
34.0ms	537×	pre	80	true
34.0ms	281×	body	80	nan
15.0ms	114×	body	80	valid

simplify148.0ms

Counts: 1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize42.0ms

Local error

Found 4 expressions with local error:

29.0b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.3b	(/ (- (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)))

rewrite41.0ms

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

24.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
14.0ms	(- (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))

series397.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(sqrt (fma c (* -3 a) (* b b)))
105.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
101.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
73.0ms	(fma c (* -3 a) (* b b))

simplify1.3s

Counts: 114 → 114

prune1.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 26.3b

localize48.0ms

Local error

Found 4 expressions with local error:

28.0b	(- (* (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))) (fma 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)))) (* b (* b b))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c)))) (* 3 a))
0.3b	(* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
48×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
12×	`pow3`
11×	`difference-cubes` `cube-unmult`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`div-sub` `associate-l` `prod-exp` `cbrt-unprod` `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 → 139

Calls

4 calls:

Slowest

60.0ms	(/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c))))
40.0ms	(/ (/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c)))) (* 3 a))
38.0ms	(- (* (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

528.0ms	(/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c))))
522.0ms	(/ (/ (- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c)))) (* 3 a))
143.0ms	(- (* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c)))) (* b (* b b)))
82.0ms	(* (fma b b (* (* a -3) c)) (sqrt (fma b b (* (* a -3) c))))

simplify1.3s

Counts: 151 → 151

prune2.3s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 2.7b

localize107.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
40×	`times-frac`
35×	`add-cbrt-cube` `add-exp-log`
27×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
20×	`pow-prod-down`
16×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-/r` `associate-l*` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-plus` `associate-r` `*-commutative`
1×	`pow2` `swap-sqr` `associate-/l/`

Counts

4 → 137

Calls

4 calls:

Slowest

37.0ms	(* (* a c) (* a c))
19.0ms	(* b (* c a))
10.0ms	(/ (/ (fma (/ (* (* a c) (* a c)) b) 27/8 (* -9/2 (* b (* c a)))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c)))) (* 3 a))
4.0ms	(/ (fma (/ (* (* a c) (* a c)) b) 27/8 (* -9/2 (* b (* c a)))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

243.0ms	(/ (/ (fma (/ (* (* a c) (* a c)) b) 27/8 (* -9/2 (* b (* c a)))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c)))) (* 3 a))
238.0ms	(/ (fma (/ (* (* a c) (* a c)) b) 27/8 (* -9/2 (* b (* c a)))) (fma b (+ (sqrt (fma b b (* (* a -3) c))) b) (fma b b (* (* a -3) c))))
56.0ms	(* (* a c) (* a c))
40.0ms	(* b (* c a))

simplify959.0ms

Counts: 149 → 149

prune2.9s

Pruning

47 alts after pruning (47 fresh and 0 done)

Merged error: 2.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* a c) (* a c))
0.4b	(/ (/ 1 a) (fma b (+ (sqrt (fma b b (* (* a c) -3))) b) (fma b b (* (* a c) -3))))
0.3b	(* (/ (fma (/ (* (* a c) (* a c)) b) 27/8 (* -9/2 (* b (* c a)))) 3) (/ (/ 1 a) (fma b (+ (sqrt (fma b b (* (* a c) -3))) b) (fma b b (* (* a c) -3)))))
0.3b	(* (* a c) -3)

rewrite461.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
117×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
89×	`add-cube-cbrt`
65×	`add-exp-log`
50×	`pow1`
47×	`add-cbrt-cube` `associate-r`
23×	`div-exp`
21×	`pow-prod-down` `prod-exp`
17×	`cbrt-unprod`
15×	`associate-l`
13×	`associate-/l*`
12×	`cbrt-undiv`
10×	`div-inv`
8×	`unswap-sqr`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `associate-/r` `1-exp` `-commutative`
2×	`pow-plus`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `swap-sqr` `associate-l/` `associate-r/` `associate-/l/`

Counts

4 → 228

Calls

4 calls:

Slowest

401.0ms	(* (/ (fma (/ (* (* a c) (* a c)) b) 27/8 (* -9/2 (* b (* c a)))) 3) (/ (/ 1 a) (fma b (+ (sqrt (fma b b (* (* a c) -3))) b) (fma b b (* (* a c) -3)))))
26.0ms	(* (* a c) -3)
22.0ms	(* (* a c) (* a c))
7.0ms	(/ (/ 1 a) (fma b (+ (sqrt (fma b b (* (* a c) -3))) b) (fma b b (* (* a c) -3))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

398.0ms	(/ (/ 1 a) (fma b (+ (sqrt (fma b b (* (* a c) -3))) b) (fma b b (* (* a c) -3))))
264.0ms	(* (/ (fma (/ (* (* a c) (* a c)) b) 27/8 (* -9/2 (* b (* c a)))) 3) (/ (/ 1 a) (fma b (+ (sqrt (fma b b (* (* a c) -3))) b) (fma b b (* (* a c) -3)))))
39.0ms	(* (* a c) (* a c))
22.0ms	(* (* a c) -3)

simplify2.0s

Counts: 240 → 240

prune4.2s

Pruning

49 alts after pruning (49 fresh and 0 done)

Merged error: 2.2b

regimes1.3s

Accuracy

23.7% (6.9b remaining)

Error of 9.2b against oracle of 2.3b and baseline of 11.3b

bsearch77.0ms

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.7s	4483×	body	160	valid
1.2s	8690×	body	80	nan
1.1s	16690×	pre	80	true
531.0ms	3517×	body	80	valid