Details

sample115.0ms

Algorithm

intervals

Results

29.0ms	40×	body	2560	valid
24.0ms	187×	body	80	valid
24.0ms	32×	body	1280	valid
11.0ms	96×	body	80	nan
4.0ms	8×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify113.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
1.1b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.2b	(- (* b b) (* (* 3 a) c))
20.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

105.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
54.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
13.0ms	(- (* b b) (* (* 3 a) c))
11.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
94.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
53.0ms	(- (* b b) (* (* 3 a) c))
89.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.1s

Counts

84 → 84

Iterations

Iter	Nodes
3	4778
2	1240
1	393
0	153

prune828.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* 3 a) c)
1.1b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.2b	(- (* b b) (* (* 3 a) c))
20.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

12.0ms	(* (* 3 a) c)
51.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
6.0ms	(- (* b b) (* (* 3 a) c))
6.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 3 a) c)
119.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
78.0ms	(- (* b b) (* (* 3 a) c))
92.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
3	3293
2	936
1	290
0	119

prune767.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (* a c))
1.1b	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
1.2b	(- (* b b) (* 3 (* a c)))
20.1b	(sqrt (- (* b b) (* 3 (* a c))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

18.0ms	(* 3 (* a c))
30.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
8.0ms	(- (* b b) (* 3 (* a c)))
11.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 3 (* a c))
112.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
58.0ms	(- (* b b) (* 3 (* a c)))
93.0ms	(sqrt (- (* b b) (* 3 (* a c))))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
3	2600
2	773
1	275
0	116

prune776.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* 3 a))
1.1b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.2b	(- (* b b) (* (* 3 a) c))
20.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

13.0ms	(/ 1 (* 3 a))
51.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
10.0ms	(- (* b b) (* (* 3 a) c))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1 (* 3 a))
114.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
54.0ms	(- (* b b) (* (* 3 a) c))
106.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.8s

Counts

82 → 82

Iterations

Iter	Nodes
3	3420
2	964
1	317
0	136

prune760.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

regimes477.0ms

Accuracy

84.6% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.3b

bsearch195.0ms

Steps

Iters	Range		Point
8	1.248337945535211e-66	3.048951962881303e-62	3.0168583404714427e-66
8	-6.399945091756968e+81	-6.440043566032316e+77	-4.724852789705704e+81

simplify7.0ms

Iterations

Iter	Nodes
2	32
1	32
0	27

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.4s	1086×	body	2560	valid
736.0ms	5910×	body	80	valid
575.0ms	919×	body	1280	valid
313.0ms	2909×	body	80	nan
176.0ms	435×	body	640	valid
165.0ms	119×	body	5120	valid
86.0ms	214×	body	320	valid
22.0ms	108×	body	160	valid