Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	59×	body	1280	valid
6.0ms	34×	body	640	valid
6.0ms	122×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	16×	body	160	valid

simplify241.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	350
14	350
13	346
12	340
11	329
10	222
9	96
8	75
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
4.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

963×	`*-un-lft-identity`
724×	`times-frac`
575×	`add-sqr-sqrt`
468×	`prod-diff`
409×	`add-cube-cbrt`
185×	`distribute-lft-out`
92×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
46×	`div-inv`
28×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
5×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`

Counts

2 → 561

Calls

2 calls:

27.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series196.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (+ x 1.0) (- x 1.0))
142.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.5s

Counts

567 → 567

Iterations

Iter	Nodes
done	5003
2	2984
1	1192
0	502

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (/ 1 (* x x)) 1.0 (/ 3.0 x))
0.5b	(/ 1 (* x x))
0.5b	(/ 1 (* x x))
7.8b	(fma (/ 3.0 x) (/ 1 (* x x)) (fma (/ 1 (* x x)) 1.0 (/ 3.0 x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
20×	`pow1`
14×	`add-cbrt-cube`
12×	`pow-flip`
8×	`add-sqr-sqrt` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
6×	`times-frac` `prod-exp` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 88

Calls

4 calls:

0.0ms	(fma (/ 1 (* x x)) 1.0 (/ 3.0 x))
16.0ms	(/ 1 (* x x))
23.0ms	(/ 1 (* x x))
1.0ms	(fma (/ 3.0 x) (/ 1 (* x x)) (fma (/ 1 (* x x)) 1.0 (/ 3.0 x)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma (/ 1 (* x x)) 1.0 (/ 3.0 x))
22.0ms	(/ 1 (* x x))
18.0ms	(/ 1 (* x x))
39.0ms	(fma (/ 3.0 x) (/ 1 (* x x)) (fma (/ 1 (* x x)) 1.0 (/ 3.0 x)))

simplify1.7s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	1490
2	452
1	178
0	85

prune453.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
4.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
4.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

2721×	`*-un-lft-identity`
1732×	`times-frac`
1190×	`add-sqr-sqrt`
936×	`prod-diff`
805×	`add-cube-cbrt`
510×	`distribute-lft-out`
405×	`distribute-lft-out--`
202×	`sqrt-prod`
180×	`associate-/r/`
172×	`difference-of-squares`
90×	`div-inv`
79×	`swap-sqr`
54×	`flip3-+` `flip-+`
47×	`flip3--` `flip--`
36×	`fma-neg`
27×	`sqrt-div`
20×	`pow1`
19×	`associate-r` `associate-l`
11×	`frac-sub`
9×	`frac-times` `sqrt-pow1` `pow1/2`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr`
2×	`sub-neg` `diff-log`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 1222

Calls

4 calls:

156.0ms	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
587.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
171.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series650.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
150.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
146.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
143.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.6s

Counts

1234 → 1234

Iterations

Iter	Nodes
done	5001
2	3228
1	1334
0	599

prune5.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
4.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
4.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
4.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

2885×	`*-un-lft-identity`
2152×	`times-frac`
1703×	`add-sqr-sqrt`
1404×	`prod-diff`
1197×	`add-cube-cbrt`
553×	`distribute-lft-out`
281×	`distribute-lft-out--`
270×	`associate-/r/`
236×	`difference-of-squares`
135×	`div-inv`
81×	`flip3-+` `flip-+`
65×	`flip3--` `flip--`
61×	`sqrt-prod`
54×	`fma-neg`
36×	`sqrt-div`
22×	`associate-l`
19×	`associate-r`
16×	`pow1`
12×	`sqrt-pow1`
11×	`frac-sub`
10×	`add-log-exp`
9×	`frac-times`
8×	`pow1/2`
6×	`add-cbrt-cube` `add-exp-log` `pow-prod-up` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `pow-prod-down` `associate-l/` `associate-r/`
2×	`pow-plus` `cube-unmult`
1×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 1630

Calls

4 calls:

633.0ms	(* (sqrt (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
162.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
195.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
174.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

413.0ms	(* (sqrt (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
190.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
207.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
193.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify4.1s

Counts

1642 → 1642

Iterations

Iter	Nodes
done	5000
2	3706
1	1434
0	634

prune9.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes131.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.6b

bsearch138.0ms

Steps

Iters	Range		Point
9	28.34319947931986	37605091470.942024	6872.825457982199
8	-137985211.42758197	-2980.3304644899954	-7470.879892531778

simplify11.0ms

Iterations

Iter	Nodes
done	46
2	46
1	42
0	31

end0.0ms

sample1.2s

Algorithm

intervals

Results

470.0ms	1751×	body	1280	valid
247.0ms	4073×	body	80	valid
220.0ms	1201×	body	640	valid
72.0ms	659×	body	320	valid
23.0ms	316×	body	160	valid