Details

sample112.0ms

Algorithm

intervals

Results

32.0ms	192×	body	80	valid
20.0ms	37×	body	2560	valid
12.0ms	30×	body	1280	valid
7.0ms	81×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify67.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	128
5	128
4	119
3	86
2	46
1	25
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite110.0ms

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` `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 → 90

Calls

4 calls:

53.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
52.0ms	(- (* b b) (* (* 4.0 a) c))
90.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2115
1	450
0	167

prune640.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
4.1b	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
10.0b	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
22.4b	(sqrt (fma (* a c) (- 4.0) (* b b)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `div-inv` `flip--`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `diff-log` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 230

Calls

4 calls:

23.0ms	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
69.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
64.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
3.0ms	(sqrt (fma (* a c) (- 4.0) (* b b)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
333.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
273.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
138.0ms	(sqrt (fma (* a c) (- 4.0) (* b b)))

simplify1.8s

Counts

242 → 242

Iterations

Iter	Nodes
done	5000
2	4024
1	778
0	319

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma b b (* (- a) (* 4.0 c)))
0.9b	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
12.7b	(/ (* (* 4.0 c) a) a)
22.4b	(sqrt (fma b b (* (- a) (* 4.0 c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `div-exp` `prod-exp` `cbrt-unprod`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `div-inv` `flip--` `associate-/l*`

Counts

4 → 140

Calls

4 calls:

0.0ms	(fma b b (* (- a) (* 4.0 c)))
22.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
15.0ms	(/ (* (* 4.0 c) a) a)
1.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma b b (* (- a) (* 4.0 c)))
101.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
10.0ms	(/ (* (* 4.0 c) a) a)
106.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

simplify1.3s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	2590
1	505
0	212

prune766.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ 1 (* 4.0 c)))
0.8b	(fma b b (* (- a) (* 4.0 c)))
0.9b	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
22.4b	(sqrt (fma b b (* (- a) (* 4.0 c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
62×	`add-cube-cbrt`
60×	`prod-diff`
47×	`add-exp-log`
34×	`sqrt-prod`
33×	`times-frac`
26×	`div-exp`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`rec-exp` `add-cbrt-cube` `1-exp`
10×	`fma-neg`
9×	`pow1` `prod-exp`
8×	`add-log-exp`
7×	`associate-/r*` `neg-mul-1`
6×	`pow-flip`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`diff-log` `distribute-lft-out--` `inv-pow` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `neg-log` `associate-/r/` `cbrt-unprod` `fma-udef` `flip--` `remove-double-div`

Counts

4 → 189

Calls

4 calls:

16.0ms	(/ 1 (/ 1 (* 4.0 c)))
0.0ms	(fma b b (* (- a) (* 4.0 c)))
23.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
2.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (/ 1 (* 4.0 c)))
85.0ms	(fma b b (* (- a) (* 4.0 c)))
137.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
118.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

simplify1.5s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
2	2951
1	652
0	270

prune609.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

regimes463.0ms

Accuracy

94.5% (1.3b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 29.5b

bsearch247.0ms

Steps

Iters	Range	Point
9	3.768382185355077e+69	1.107955803311012e+78	4.2871760960662547e+77
3	-5.1570355596853615e-201	-3.8052178173245655e-201	-4.565615297402514e-201
8	-1.0455781936591884e+110	-3.8601914758440924e+107	-4.065832835277421e+109

Iters

Range

Point

3.768382185355077e+69

1.107955803311012e+78

4.2871760960662547e+77

-5.1570355596853615e-201

-3.8052178173245655e-201

-4.565615297402514e-201

-1.0455781936591884e+110

-3.8601914758440924e+107

-4.065832835277421e+109

simplify6.0ms

Iterations

Iter	Nodes
done	56
1	56
0	44

end0.0ms

sample3.4s

Algorithm

intervals

Results

825.0ms	2814×	body	80	nan
627.0ms	1070×	body	2560	valid
574.0ms	5837×	body	80	valid
496.0ms	936×	body	1280	valid
183.0ms	453×	body	640	valid
55.0ms	94×	body	5120	valid
49.0ms	223×	body	320	valid
17.0ms	113×	body	160	valid