Details

sample111.0ms

Algorithm

intervals

Results

34.0ms	195×	body	80	valid
15.0ms	34×	body	1280	valid
10.0ms	18×	body	2560	valid
9.0ms	107×	body	80	nan
5.0ms	13×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid

simplify220.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	75
2	40
1	22
0	12

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
0.9b	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
1.0b	(- (* b b) (* (* a 3.0) c))
21.8b	(sqrt (- (* b b) (* (* a 3.0) c)))

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

201.0ms	(/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
106.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
18.0ms	(- (* b b) (* (* a 3.0) c))
32.0ms	(sqrt (- (* b b) (* (* a 3.0) c)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
187.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
93.0ms	(- (* b b) (* (* a 3.0) c))
127.0ms	(sqrt (- (* b b) (* (* a 3.0) c)))

simplify3.1s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	1532
1	514
0	195

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* a 3.0))
0.9b	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
1.0b	(- (* b b) (* (* a 3.0) c))
21.8b	(sqrt (- (* b b) (* (* a 3.0) c)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1` `add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`flip3--` `times-frac` `prod-exp` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `pow-flip` `sqrt-div` `diff-log` `1-exp` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 104

Calls

4 calls:

25.0ms	(/ 1 (* a 3.0))
124.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
19.0ms	(- (* b b) (* (* a 3.0) c))
26.0ms	(sqrt (- (* b b) (* (* a 3.0) c)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1 (* a 3.0))
236.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
103.0ms	(- (* b b) (* (* a 3.0) c))
151.0ms	(sqrt (- (* b b) (* (* a 3.0) c)))

simplify5.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	4741
2	1149
1	439
0	178

prune801.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* a 3.0) (- (sqrt (- (* b b) (* (* a 3.0) c))) b))
0.9b	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
1.0b	(- (* b b) (* (* a 3.0) c))
21.8b	(sqrt (- (* b b) (* (* a 3.0) c)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/r*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

88.0ms	(/ (* a 3.0) (- (sqrt (- (* b b) (* (* a 3.0) c))) b))
95.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
18.0ms	(- (* b b) (* (* a 3.0) c))
23.0ms	(sqrt (- (* b b) (* (* a 3.0) c)))

series788.0ms

Counts

4 → 12

Calls

4 calls:

403.0ms	(/ (* a 3.0) (- (sqrt (- (* b b) (* (* a 3.0) c))) b))
154.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
86.0ms	(- (* b b) (* (* a 3.0) c))
145.0ms	(sqrt (- (* b b) (* (* a 3.0) c)))

simplify2.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1513
1	491
0	186

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) 3.0))
0.9b	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
1.0b	(- (* b b) (* (* a 3.0) c))
21.8b	(sqrt (- (* b b) (* (* a 3.0) c)))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
36×	`add-cube-cbrt`
34×	`times-frac`
26×	`add-exp-log`
22×	`associate-r`
19×	`prod-diff` `sqrt-prod`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `fma-neg`
6×	`unswap-sqr`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 141

Calls

4 calls:

177.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) 3.0))
110.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
15.0ms	(- (* b b) (* (* a 3.0) c))
27.0ms	(sqrt (- (* b b) (* (* a 3.0) c)))

series746.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) 3.0))
209.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)
99.0ms	(- (* b b) (* (* a 3.0) c))
143.0ms	(sqrt (- (* b b) (* (* a 3.0) c)))

simplify3.1s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	2081
1	684
0	248

prune1.1s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 5.9b

regimes715.0ms

Accuracy

81.6% (5.4b remaining)

Error of 10.8b against oracle of 5.5b and baseline of 34.7b

bsearch235.0ms

Steps

Iters	Range		Point
9	1.177766511972955e-157	7.998381519079639e-153	7.923524897992037e-153
10	-8.514648891065421e+79	-9.051599321779201e+64	-1.6964502144974645e+75

simplify10.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	5752×	body	80	valid
775.0ms	1081×	body	2560	valid
541.0ms	924×	body	1280	valid
366.0ms	2817×	body	80	nan
323.0ms	480×	body	640	valid
125.0ms	97×	body	5120	valid
61.0ms	238×	body	320	valid
20.0ms	120×	body	160	valid