Details

sample97.0ms

Algorithm

intervals

Results

25.0ms	35×	body	2560	valid
20.0ms	191×	body	80	valid
10.0ms	23×	body	1280	valid
9.0ms	101×	body	80	nan
7.0ms	18×	body	640	valid
4.0ms	5×	body	5120	valid
2.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid

simplify143.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize43.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (- (* b b) (* (* 3 a) c)))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.6b	(- (* b b) (* (* 3 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

Slowest

68.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
16.0ms	(- (* b b) (* (* 3 a) c))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
119.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
114.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
61.0ms	(- (* b b) (* (* 3 a) c))

simplify2.2s

Counts: 106 → 106

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize43.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (- (* b b) (* (* 3 a) c)))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.6b	(- (* b b) (* (* 3 a) c))
0.2b	(/ (* 3 a) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

Slowest

30.0ms	(/ (* 3 a) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))))
16.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
9.0ms	(- (* b b) (* (* 3 a) c))

series470.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

233.0ms	(/ (* 3 a) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))))
107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
55.0ms	(- (* b b) (* (* 3 a) c))

simplify1.7s

Counts: 105 → 105

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

localize36.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (- (* b b) (* (* a c) 3)))
1.6b	(- (sqrt (- (* b b) (* (* a c) 3))) b)
0.6b	(- (* b b) (* (* a c) 3))
0.3b	(* (/ 1 3) (/ (- (sqrt (- (* b b) (* (* a c) 3))) b) a))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

Slowest

70.0ms	(* (/ 1 3) (/ (- (sqrt (- (* b b) (* (* a c) 3))) b) a))
42.0ms	(- (sqrt (- (* b b) (* (* a c) 3))) b)
13.0ms	(- (* b b) (* (* a c) 3))
10.0ms	(sqrt (- (* b b) (* (* a c) 3)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

175.0ms	(* (/ 1 3) (/ (- (sqrt (- (* b b) (* (* a c) 3))) b) a))
130.0ms	(- (sqrt (- (* b b) (* (* a c) 3))) b)
93.0ms	(sqrt (- (* b b) (* (* a c) 3)))
53.0ms	(- (* b b) (* (* a c) 3))

simplify924.0ms

Counts: 157 → 157

prune2.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.1b

localize60.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (- (* b b) (* (* a c) 3)))
1.6b	(- (sqrt (- (* b b) (* (* a c) 3))) b)
1.0b	(/ (sqrt 1) (cbrt 3))
0.6b	(- (* b b) (* (* a c) 3))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
36×	`times-frac`
21×	`cbrt-prod`
19×	`prod-diff`
8×	`add-log-exp`
7×	`fma-neg`
6×	`associate-/r` `add-exp-log` `associate-/l`
5×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv` `distribute-lft-out--`

Counts

4 → 140

Calls

4 calls:

Slowest

45.0ms	(- (sqrt (- (* b b) (* (* a c) 3))) b)
11.0ms	(- (* b b) (* (* a c) 3))
10.0ms	(sqrt (- (* b b) (* (* a c) 3)))
5.0ms	(/ (sqrt 1) (cbrt 3))

series249.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

104.0ms	(sqrt (- (* b b) (* (* a c) 3)))
86.0ms	(- (sqrt (- (* b b) (* (* a c) 3))) b)
59.0ms	(- (* b b) (* (* a c) 3))
0.0ms	(/ (sqrt 1) (cbrt 3))

simplify1.3s

Counts: 150 → 150

prune2.7s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.1b

regimes944.0ms

Accuracy

86.6% (3.7b remaining)

Error of 9.0b against oracle of 5.2b and baseline of 33.2b

bsearch321.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	1091×	body	2560	valid
1.1s	927×	body	1280	valid
919.0ms	5802×	body	80	valid
390.0ms	2924×	body	80	nan
293.0ms	444×	body	640	valid
167.0ms	134×	body	5120	valid
84.0ms	221×	body	320	valid
25.0ms	104×	body	160	valid