Details

sample123.0ms

Algorithm

intervals

Results

39.0ms	186×	body	80	valid
24.0ms	29×	body	2560	valid
15.0ms	24×	body	1280	valid
11.0ms	88×	body	80	nan
8.0ms	17×	body	640	valid
4.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid

simplify98.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.6b	(- (* b b) (* (* 3 a) c))
24.4b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite117.0ms

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:

72.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
8.0ms	(- (* b b) (* (* 3 a) c))
13.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
109.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
65.0ms	(- (* b b) (* (* 3 a) c))
107.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify4.3s

Counts

106 → 106

Iterations

Iter	Nodes
3	4953
2	1375
1	440
0	170

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) a)
1.0b	(- (sqrt (fma -3 (* a c) (* b b))) b)
1.7b	(fma -3 (* a c) (* b b))
24.4b	(sqrt (fma -3 (* a c) (* b b)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

34.0ms	(/ (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) a)
17.0ms	(- (sqrt (fma -3 (* a c) (* b b))) b)
0.0ms	(fma -3 (* a c) (* b b))
3.0ms	(sqrt (fma -3 (* a c) (* b b)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) a)
141.0ms	(- (sqrt (fma -3 (* a c) (* b b))) b)
69.0ms	(fma -3 (* a c) (* b b))
114.0ms	(sqrt (fma -3 (* a c) (* b b)))

simplify2.2s

Counts

191 → 191

Iterations

Iter	Nodes
3	4445
2	1409
1	600
0	277

prune2.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.6b	(- (* b b) (* (* 3 a) c))
24.4b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

18.0ms	(/ 1 (* 3 a))
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
16.0ms	(- (* b b) (* (* 3 a) c))
11.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (* 3 a))
123.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
67.0ms	(- (* b b) (* (* 3 a) c))
102.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.5s

Counts

106 → 106

Iterations

Iter	Nodes
3	3418
2	1066
1	381
0	155

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sqrt (fma -3 (* a c) (* b b))) 3) a)
1.7b	(fma -3 (* a c) (* b b))
4.7b	(- (/ (/ (sqrt (fma -3 (* a c) (* b b))) 3) a) (/ (/ b 3) a))
24.4b	(sqrt (fma -3 (* a c) (* b b)))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

10113×	`times-frac`
5326×	`add-sqr-sqrt`
5300×	`*-un-lft-identity`
5274×	`add-cube-cbrt`
3010×	`prod-diff`
1230×	`sqrt-prod`
469×	`div-inv`
70×	`fma-neg`
22×	`associate-/l*`
13×	`distribute-lft-out--`
12×	`difference-of-squares`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-out--` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `fma-udef` `flip--` `sub-div` `associate-/l/`

Counts

4 → 3262

Calls

4 calls:

18.0ms	(/ (/ (sqrt (fma -3 (* a c) (* b b))) 3) a)
1.0ms	(fma -3 (* a c) (* b b))
80.0ms	(- (/ (/ (sqrt (fma -3 (* a c) (* b b))) 3) a) (/ (/ b 3) a))
2.0ms	(sqrt (fma -3 (* a c) (* b b)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (/ (sqrt (fma -3 (* a c) (* b b))) 3) a)
71.0ms	(fma -3 (* a c) (* b b))
146.0ms	(- (/ (/ (sqrt (fma -3 (* a c) (* b b))) 3) a) (/ (/ b 3) a))
146.0ms	(sqrt (fma -3 (* a c) (* b b)))

simplify6.3s

Counts

3274 → 3274

Iterations

Iter	Nodes
1	6666
0	3156

prune1.1m

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.4b

regimes1.1s

Accuracy

83% (4.8b remaining)

Error of 10.7b against oracle of 5.9b and baseline of 34.1b

bsearch249.0ms

Steps

Iters	Range		Point
9	2.5177836961106285e-119	1.1213560046341023e-113	1.1094847447691107e-113
9	-1.1584173197036289e+58	-1.9532574545037316e+51	-1.1446001462836007e+58

simplify11.0ms

Iterations

Iter	Nodes
2	40
1	40
0	33

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	5837×	body	80	valid
1.1s	1091×	body	2560	valid
612.0ms	912×	body	1280	valid
349.0ms	2906×	body	80	nan
261.0ms	460×	body	640	valid
133.0ms	126×	body	5120	valid
131.0ms	227×	body	320	valid
25.0ms	98×	body	160	valid