Details

sample87.0ms

Algorithm

intervals

Results

21.0ms	41×	body	2560	valid
15.0ms	178×	body	80	valid
12.0ms	29×	body	1280	valid
8.0ms	93×	body	80	nan
5.0ms	17×	body	640	valid
1.0ms	5×	body	160	valid
1.0ms	1×	body	5120	valid
1.0ms	2×	body	320	valid

simplify87.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	79
2	43
1	25
0	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite122.0ms

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:

72.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
93.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5002
2	1448
1	442
0	167

prune700.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
1.7b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 152

Calls

4 calls:

53.0ms	(/ 1 (/ (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
63.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(/ 1 (/ (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
114.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
51.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

164 → 164

Iterations

Iter	Nodes
done	5004
2	2030
1	660
0	261

prune870.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* a 2.0) (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)))
1.7b	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
2.5b	(fma b b (- (* (* 4.0 a) c)))
23.9b	(sqrt (fma b b (- (* (* 4.0 a) c))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
18×	`prod-diff`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`difference-of-squares`
9×	`associate-/r/`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`cbrt-undiv` `flip3--` `div-inv` `flip--` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `cbrt-unprod` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 144

Calls

4 calls:

21.0ms	(/ 1 (/ (* a 2.0) (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)))
17.0ms	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
1.0ms	(fma b b (- (* (* 4.0 a) c)))
3.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ 1 (/ (* a 2.0) (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)))
135.0ms	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
77.0ms	(fma b b (- (* (* 4.0 a) c)))
152.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))

simplify2.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	1687
1	568
0	239

prune905.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* a 2.0)) (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b))
1.7b	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
2.5b	(fma b b (- (* (* 4.0 a) c)))
23.9b	(sqrt (fma b b (- (* (* 4.0 a) c))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
54×	`prod-diff`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-cbrt-cube`
10×	`prod-exp`
7×	`pow1` `associate-l`
6×	`fma-neg` `associate-r` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `times-frac` `flip3--` `flip--`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*r/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

57.0ms	(* (/ 1 (* a 2.0)) (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b))
9.0ms	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
0.0ms	(fma b b (- (* (* 4.0 a) c)))
1.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (/ 1 (* a 2.0)) (- (sqrt (fma b b (- (* (* 4.0 a) c)))) b))
126.0ms	(- (sqrt (fma b b (- (* (* 4.0 a) c)))) b)
100.0ms	(fma b b (- (* (* 4.0 a) c)))
108.0ms	(sqrt (fma b b (- (* (* 4.0 a) c))))

simplify2.0s

Counts

158 → 158

Iterations

Iter	Nodes
done	5004
2	1816
1	628
0	226

prune759.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.0b

regimes463.0ms

Accuracy

85.3% (4.3b remaining)

Error of 10.1b against oracle of 5.8b and baseline of 34.9b

bsearch238.0ms

Steps

Iters	Range		Point
10	8.767897341253802e-114	4.657027509742155e-104	4.6129908231112306e-104
9	-6.117539429929052e+154	-3.6285784997486435e+148	-3.6803290429888884e+148

simplify17.0ms

Iterations

Iter	Nodes
done	48
2	48
1	40
0	28

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	1115×	body	2560	valid
757.0ms	2954×	body	80	nan
535.0ms	5809×	body	80	valid
336.0ms	902×	body	1280	valid
170.0ms	454×	body	640	valid
93.0ms	105×	body	5120	valid
45.0ms	210×	body	320	valid
19.0ms	126×	body	160	valid