Details

sample164.0ms

Algorithm

intervals

Results

53.0ms	32×	body	1280	valid
35.0ms	40×	body	2560	valid
27.0ms	187×	body	80	valid
13.0ms	96×	body	80	nan
4.0ms	8×	body	640	valid
2.0ms	2×	body	5120	valid
2.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify141.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a -4) c)
1.1b	(- (sqrt (fma b b (* (* a -4) c))) b)
1.5b	(fma b b (* (* a -4) c))
20.1b	(sqrt (fma b b (* (* a -4) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

15.0ms	(* (* a -4) c)
13.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms	(fma b b (* (* a -4) c))
3.0ms	(sqrt (fma b b (* (* a -4) c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* a -4) c)
166.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
84.0ms	(fma b b (* (* a -4) c))
108.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.7s

Counts

98 → 98

Iterations

Iter	Nodes
3	2736
2	835
1	316
0	142

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.3b

localize50.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (sqrt (fma (* c -4) a (* b b))) b) a)
1.1b	(- (sqrt (fma (* c -4) a (* b b))) b)
20.1b	(sqrt (fma (* c -4) a (* b b)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 100

Calls

3 calls:

16.0ms	(/ (- (sqrt (fma (* c -4) a (* b b))) b) a)
14.0ms	(- (sqrt (fma (* c -4) a (* b b))) b)
2.0ms	(sqrt (fma (* c -4) a (* b b)))

series412.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(/ (- (sqrt (fma (* c -4) a (* b b))) b) a)
131.0ms	(- (sqrt (fma (* c -4) a (* b b))) b)
128.0ms	(sqrt (fma (* c -4) a (* b b)))

simplify2.2s

Counts

109 → 109

Iterations

Iter	Nodes
4	4487
3	1669
2	638
1	292
0	141

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (sqrt (fma (* c -4) a (* b b))) b)
5.0b	(/ (/ (* (* c -4) a) (+ (sqrt (fma (* c -4) a (* b b))) b)) a)
7.1b	(/ (* (* c -4) a) (+ (sqrt (fma (* c -4) a (* b b))) b))
20.1b	(sqrt (fma (* c -4) a (* b b)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
42×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/l*`
10×	`cbrt-undiv` `div-exp` `associate-/r/`
7×	`associate-/r*` `distribute-lft-out`
6×	`fma-def` `flip3-+` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 128

Calls

4 calls:

12.0ms	(+ (sqrt (fma (* c -4) a (* b b))) b)
33.0ms	(/ (/ (* (* c -4) a) (+ (sqrt (fma (* c -4) a (* b b))) b)) a)
23.0ms	(/ (* (* c -4) a) (+ (sqrt (fma (* c -4) a (* b b))) b))
1.0ms	(sqrt (fma (* c -4) a (* b b)))

series760.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (sqrt (fma (* c -4) a (* b b))) b)
232.0ms	(/ (/ (* (* c -4) a) (+ (sqrt (fma (* c -4) a (* b b))) b)) a)
294.0ms	(/ (* (* c -4) a) (+ (sqrt (fma (* c -4) a (* b b))) b))
113.0ms	(sqrt (fma (* c -4) a (* b b)))

simplify644.0ms

Counts

140 → 140

Iterations

Iter	Nodes
2	2045
1	577
0	216

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ (* c -4) 1) (+ (sqrt (fma a (* c -4) (* b b))) b)) 2)
0.1b	(/ (/ (* c -4) 1) (+ (sqrt (fma a (* c -4) (* b b))) b))
1.4b	(+ (sqrt (fma a (* c -4) (* b b))) b)
20.1b	(sqrt (fma a (* c -4) (* b b)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

305×	`times-frac`
198×	`*-un-lft-identity`
125×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
41×	`associate-/l*`
39×	`add-exp-log`
37×	`distribute-lft-out`
27×	`add-cbrt-cube` `div-inv`
24×	`div-exp`
14×	`cbrt-undiv`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `1-exp` `prod-exp` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

4 → 259

Calls

4 calls:

30.0ms	(/ (/ (/ (* c -4) 1) (+ (sqrt (fma a (* c -4) (* b b))) b)) 2)
15.0ms	(/ (/ (* c -4) 1) (+ (sqrt (fma a (* c -4) (* b b))) b))
8.0ms	(+ (sqrt (fma a (* c -4) (* b b))) b)
2.0ms	(sqrt (fma a (* c -4) (* b b)))

series721.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(/ (/ (/ (* c -4) 1) (+ (sqrt (fma a (* c -4) (* b b))) b)) 2)
255.0ms	(/ (/ (* c -4) 1) (+ (sqrt (fma a (* c -4) (* b b))) b))
113.0ms	(+ (sqrt (fma a (* c -4) (* b b))) b)
107.0ms	(sqrt (fma a (* c -4) (* b b)))

simplify989.0ms

Counts

271 → 271

Iterations

Iter	Nodes
2	2304
1	903
0	379

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

regimes307.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.0b

bsearch400.0ms

Steps

Iters	Range	Point
9	1.5347927881719531e+137	5.414027326126016e+143	1.2859619246531207e+138
7	1.4554634128686194e-286	8.018936905256056e-285	2.051368100893223e-286
8	-6.440043566032316e+77	-5.00182377876139e+74	-1.3798449810939068e+76

Iters

Range

Point

1.5347927881719531e+137

5.414027326126016e+143

1.2859619246531207e+138

1.4554634128686194e-286

8.018936905256056e-285

2.051368100893223e-286

-6.440043566032316e+77

-5.00182377876139e+74

-1.3798449810939068e+76

simplify19.0ms

Iterations

Iter	Nodes
2	45
1	45
0	41

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.3s	1086×	body	2560	valid
1.1s	5910×	body	80	valid
664.0ms	918×	body	1280	valid
406.0ms	2909×	body	80	nan
207.0ms	434×	body	640	valid
99.0ms	216×	body	320	valid
91.0ms	119×	body	5120	valid
24.0ms	109×	body	160	valid