Details

sample83.0ms

Algorithm

intervals

Results

18.0ms	205×	body	80	valid
15.0ms	31×	body	2560	valid
12.0ms	31×	body	1280	valid
7.0ms	89×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify115.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	164
6	164
5	160
4	153
3	121
2	64
1	29
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* (- a) c) 4.0 (* b b))
0.1b	(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
0.7b	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
19.5b	(sqrt (fma (* (- a) c) 4.0 (* b b)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `sqrt-prod` `distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 69

Calls

4 calls:

0.0ms	(fma (* (- a) c) 4.0 (* b b))
29.0ms	(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
12.0ms	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
3.0ms	(sqrt (fma (* (- a) c) 4.0 (* b b)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(fma (* (- a) c) 4.0 (* b b))
157.0ms	(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
118.0ms	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
145.0ms	(sqrt (fma (* (- a) c) 4.0 (* b b)))

simplify753.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1068
1	305
0	124

prune666.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a (* (- c) 4.0)) (* b b))
0.1b	(/ (+ b (sqrt (+ (* a (* (- c) 4.0)) (* b b)))) (* 2.0 a))
0.7b	(+ b (sqrt (+ (* a (* (- c) 4.0)) (* b b))))
19.5b	(sqrt (+ (* a (* (- c) 4.0)) (* b b)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
8×	`add-cube-cbrt` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `times-frac` `flip-+` `log1p-expm1-u` `associate-/l*`
3×	`sqrt-prod` `distribute-lft-out`
2×	`cbrt-undiv` `+-commutative` `sum-log` `sqrt-div` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 75

Calls

4 calls:

32.0ms	(+ (* a (* (- c) 4.0)) (* b b))
193.0ms	(/ (+ b (sqrt (+ (* a (* (- c) 4.0)) (* b b)))) (* 2.0 a))
44.0ms	(+ b (sqrt (+ (* a (* (- c) 4.0)) (* b b))))
24.0ms	(sqrt (+ (* a (* (- c) 4.0)) (* b b)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (* a (* (- c) 4.0)) (* b b))
132.0ms	(/ (+ b (sqrt (+ (* a (* (- c) 4.0)) (* b b)))) (* 2.0 a))
139.0ms	(+ b (sqrt (+ (* a (* (- c) 4.0)) (* b b))))
131.0ms	(sqrt (+ (* a (* (- c) 4.0)) (* b b)))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
done	5002
2	1723
1	396
0	141

prune674.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))) (* a (- 2.0)))
0.7b	(+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))
19.5b	(sqrt (fma (* (- 4.0) a) c (pow b 2)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

49.0ms	(/ (- (+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))) (* a (- 2.0)))
9.0ms	(+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))
1.0ms	(sqrt (fma (* (- 4.0) a) c (pow b 2)))

series375.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(/ (- (+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))) (* a (- 2.0)))
124.0ms	(+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))
114.0ms	(sqrt (fma (* (- 4.0) a) c (pow b 2)))

simplify930.0ms

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1473
1	366
0	147

prune702.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.1b

localize54.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- (+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))) (/ (/ 1 (- 2.0)) a))
0.7b	(+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))
19.5b	(sqrt (fma (* (- 4.0) a) c (pow b 2)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

197×	`times-frac`
116×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
106×	`associate-r`
103×	`add-cube-cbrt`
31×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
18×	`add-exp-log`
12×	`add-cbrt-cube` `associate-l`
10×	`neg-mul-1`
6×	`pow1` `div-exp`
5×	`prod-exp` `add-log-exp`
4×	`div-inv` `distribute-neg-frac` `unswap-sqr`
3×	`expm1-log1p-u` `cbrt-undiv` `fma-def` `flip3-+` `sqrt-prod` `cbrt-unprod` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`frac-times` `associate-*l/`
1×	`distribute-lft-neg-out` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 179

Calls

3 calls:

150.0ms	(* (- (+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))) (/ (/ 1 (- 2.0)) a))
11.0ms	(+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))
2.0ms	(sqrt (fma (* (- 4.0) a) c (pow b 2)))

series352.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(* (- (+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))) (/ (/ 1 (- 2.0)) a))
97.0ms	(+ b (sqrt (fma (* (- 4.0) a) c (pow b 2))))
117.0ms	(sqrt (fma (* (- 4.0) a) c (pow b 2)))

simplify656.0ms

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
1	1315
0	379

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

regimes484.0ms

Accuracy

85.4% (4.2b remaining)

Error of 9.5b against oracle of 5.3b and baseline of 34.2b

bsearch210.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	3.3896221835476005e+130
8	-8.904680992578465e-52	-2.849527055171251e-56	-4.356959927988237e-56

simplify793.0ms

Iterations

Iter	Nodes
done	5000
7	2227
6	989
5	496
4	235
3	127
2	89
1	63
0	34

end0.0ms

sample3.0s

Algorithm

intervals

Results

753.0ms	921×	body	1280	valid
748.0ms	1025×	body	2560	valid
530.0ms	5841×	body	80	valid
278.0ms	2877×	body	80	nan
170.0ms	457×	body	640	valid
71.0ms	122×	body	5120	valid
54.0ms	245×	body	320	valid
17.0ms	116×	body	160	valid