Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	5

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize6.0ms

Local error

Found 1 expressions with local error:

15.5b

(/ x (fma x x 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
1×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

6.0ms

(/ x (fma x x 1.0))

series118.0ms

Counts

1 → 3

Calls

1 calls:

118.0ms

(/ x (fma x x 1.0))

simplify1.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
3	1362
2	451
1	140
0	68

prune122.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

8.4b	(* (/ 1 (* (cbrt (fma x x 1.0)) (cbrt (fma x x 1.0)))) (/ x (cbrt (fma x x 1.0))))
15.9b	(cbrt (fma x x 1.0))
15.9b	(cbrt (fma x x 1.0))
15.9b	(cbrt (fma x x 1.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
25×	`*-un-lft-identity`
22×	`associate-r` `add-cube-cbrt`
21×	`cbrt-prod`
20×	`prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv` `associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`div-inv`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 111

Calls

4 calls:

59.0ms	(* (/ 1 (* (cbrt (fma x x 1.0)) (cbrt (fma x x 1.0)))) (/ x (cbrt (fma x x 1.0))))
1.0ms	(cbrt (fma x x 1.0))
1.0ms	(cbrt (fma x x 1.0))
1.0ms	(cbrt (fma x x 1.0))

series840.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (/ 1 (* (cbrt (fma x x 1.0)) (cbrt (fma x x 1.0)))) (/ x (cbrt (fma x x 1.0))))
259.0ms	(cbrt (fma x x 1.0))
261.0ms	(cbrt (fma x x 1.0))
204.0ms	(cbrt (fma x x 1.0))

simplify2.0s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	2140
1	593
0	201

prune572.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
15.4b	(sqrt (fma x x 1.0))
15.4b	(sqrt (fma x x 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(sqrt (fma x x 1.0))
2.0ms	(sqrt (fma x x 1.0))

series735.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt x)
272.0ms	(cbrt x)
91.0ms	(sqrt (fma x x 1.0))
67.0ms	(sqrt (fma x x 1.0))

simplify3.0s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
4	4894
3	1078
2	361
1	136
0	68

prune398.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ (/ 1.0 x) (* x x))))
0.1b	(/ (/ 1.0 x) (* x x))
0.2b	(/ 1.0 (pow x 5))
18.2b	(- (/ 1.0 (pow x 5)) (/ (/ 1.0 x) (* x x)))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

1917×	`times-frac`
965×	`add-sqr-sqrt`
941×	`*-un-lft-identity`
931×	`add-cube-cbrt`
850×	`prod-diff`
427×	`associate-+r+`
330×	`unpow-prod-down`
142×	`div-inv`
112×	`sqr-pow`
25×	`fma-neg`
21×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`associate-/l*`
13×	`fma-def`
12×	`difference-of-squares`
11×	`add-log-exp`
9×	`div-exp`
8×	`associate-/r*`
7×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `distribute-lft-out`
3×	`frac-add` `distribute-lft-out--`
2×	`clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `flip--`
1×	`pow-to-exp` `+-commutative` `associate-+r-` `flip3-+` `pow-exp` `flip-+` `associate-/l/`

Counts

4 → 1035

Calls

4 calls:

255.0ms	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ (/ 1.0 x) (* x x))))
18.0ms	(/ (/ 1.0 x) (* x x))
14.0ms	(/ 1.0 (pow x 5))
75.0ms	(- (/ 1.0 (pow x 5)) (/ (/ 1.0 x) (* x x)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ (/ 1.0 x) (* x x))))
82.0ms	(/ (/ 1.0 x) (* x x))
79.0ms	(/ 1.0 (pow x 5))
209.0ms	(- (/ 1.0 (pow x 5)) (/ (/ 1.0 x) (* x x)))

simplify2.8s

Counts

1047 → 1047

Iterations

Iter	Nodes
done	5003
1	2605
0	1179

prune7.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes63.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.6b

bsearch90.0ms

Steps

Iters	Range		Point
9	28.34319947931986	37605091470.942024	1028948.4366311172
8	-137985211.42758197	-2980.3304644899954	-3042.6217863072375

simplify7.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample445.0ms

Algorithm

intervals

Results

307.0ms

8000×

body

valid