Details

sample84.0ms

Algorithm

intervals

Results

18.0ms	38×	body	2560	valid
15.0ms	177×	body	80	valid
12.0ms	29×	body	1280	valid
9.0ms	15×	body	640	valid
9.0ms	108×	body	80	nan
2.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	7×	body	160	valid

simplify113.0ms

Counts: 1 → 1

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize22.0ms

Local error

Found 4 expressions with local error:

22.8b	(sqrt (fma c (* -3 a) (* b b)))
1.8b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.2b	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
0.1b	(fma c (* -3 a) (* b b))

rewrite31.0ms

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

18.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
9.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -3 a) (* b b)))
0.0ms	(fma c (* -3 a) (* b b))

series349.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

101.0ms	(sqrt (fma c (* -3 a) (* b b)))
92.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
91.0ms	(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
64.0ms	(fma c (* -3 a) (* b b))

simplify1.2s

Counts: 114 → 114

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 30.5b

localize30.0ms

Local error

Found 4 expressions with local error:

22.8b	(sqrt (fma c (* -3 a) (* b b)))
1.8b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.3b	(/ 1/3 a)
0.2b	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (/ 1/3 a))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`add-cube-cbrt`
19×	`times-frac`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `flip3--` `flip--` `associate-/l`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 130

Calls

4 calls:

Slowest

24.0ms	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (/ 1/3 a))
8.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
3.0ms	(/ 1/3 a)
2.0ms	(sqrt (fma c (* -3 a) (* b b)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

105.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
90.0ms	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (/ 1/3 a))
90.0ms	(sqrt (fma c (* -3 a) (* b b)))
21.0ms	(/ 1/3 a)

simplify1.1s

Counts: 142 → 142

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.5b

localize41.0ms

Local error

Found 4 expressions with local error:

22.8b	(sqrt (fma c (* -3 a) (* b b)))
1.8b	(- (sqrt (fma c (* -3 a) (* b b))) b)
0.4b	(* 1/3 (/ 1 a))
0.2b	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (* 1/3 (/ 1 a)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
28×	`add-exp-log` `add-cube-cbrt`
18×	`add-cbrt-cube` `prod-diff`
17×	`sqrt-prod`
14×	`associate-r`
13×	`prod-exp`
12×	`pow1`
11×	`times-frac`
9×	`associate-l`
7×	`cbrt-unprod`
6×	`fma-neg` `associate-*r/` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3--` `div-exp` `pow-prod-down` `un-div-inv` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
3×	`unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-l/` `-commutative` `distribute-lft-out--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 133

Calls

4 calls:

Slowest

43.0ms	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (* 1/3 (/ 1 a)))
17.0ms	(* 1/3 (/ 1 a))
12.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -3 a) (* b b)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(- (sqrt (fma c (* -3 a) (* b b))) b)
114.0ms	(* (- (sqrt (fma c (* -3 a) (* b b))) b) (* 1/3 (/ 1 a)))
112.0ms	(sqrt (fma c (* -3 a) (* b b)))
28.0ms	(* 1/3 (/ 1 a))

simplify1.6s

Counts: 145 → 145

prune1.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 21.6b

localize46.0ms

Local error

Found 4 expressions with local error:

22.8b	(sqrt (fma c (* -3 a) (* b b)))
14.3b	(* (/ 1/3 a) (fma c (* a -3) 0))
1.3b	(+ (sqrt (fma c (* -3 a) (* b b))) b)
0.3b	(/ 1/3 a)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`fma-def` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `distribute-lft-out`

Counts

4 → 104

Calls

4 calls:

Slowest

9.0ms	(* (/ 1/3 a) (fma c (* a -3) 0))
6.0ms	(+ (sqrt (fma c (* -3 a) (* b b))) b)
5.0ms	(/ 1/3 a)
1.0ms	(sqrt (fma c (* -3 a) (* b b)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(sqrt (fma c (* -3 a) (* b b)))
113.0ms	(+ (sqrt (fma c (* -3 a) (* b b))) b)
68.0ms	(* (/ 1/3 a) (fma c (* a -3) 0))
22.0ms	(/ 1/3 a)

simplify1.0s

Counts: 116 → 116

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.0b

regimes407.0ms

Accuracy

98.8% (0.2b remaining)

Error of 13.8b against oracle of 13.6b and baseline of 29.4b

bsearch320.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	1089×	body	2560	valid
1.2s	912×	body	1280	valid
943.0ms	5835×	body	80	valid
386.0ms	2987×	body	80	nan
235.0ms	469×	body	640	valid
112.0ms	117×	body	5120	valid
78.0ms	213×	body	320	valid
30.0ms	116×	body	160	valid