Details

sample22.0ms

Algorithm

intervals

Results

5.0ms	48×	body	640	valid
5.0ms	153×	body	80	valid
2.0ms	16×	body	1280	valid
2.0ms	24×	body	320	valid
1.0ms	15×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
49.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
222.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1.0 (+ x 1.0))
32.0ms	(/ 1.0 (- x 1.0))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
227.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify148.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- x 1.0))
0.2b	(cbrt (- x 1.0))
0.2b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
15.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

370×	`*-un-lft-identity`
332×	`times-frac`
277×	`add-sqr-sqrt`
245×	`add-cube-cbrt`
236×	`associate-+l+`
234×	`prod-diff`
45×	`distribute-lft-out`
38×	`cbrt-prod`
31×	`div-inv`
26×	`associate-/r/`
16×	`cbrt-div`
14×	`flip3-+` `flip-+` `distribute-lft-out--`
11×	`pow1`
10×	`fma-def` `swap-sqr` `difference-of-squares`
9×	`flip3--` `flip--` `add-log-exp`
8×	`pow1/3` `associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`frac-add`
2×	`associate-r/` `pow-prod-down` `associate-l/` `sum-log` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `associate-+l-` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod`

Counts

4 → 360

Calls

4 calls:

2.0ms	(cbrt (- x 1.0))
2.0ms	(cbrt (- x 1.0))
19.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
280.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (- x 1.0))
101.0ms	(cbrt (- x 1.0))
123.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
253.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (/ 1.0 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify130.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	809	6667
1	3181	5608
2	5002	3221

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
0.1b	(/ 2.0 (pow x 3))
0.2b	(/ 1 (pow x 7))
0.3b	(/ 1 (pow x 5))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
27×	`add-exp-log`
26×	`associate-/r*`
15×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`pow-to-exp` `pow-exp`
6×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-flip` `inv-pow`
1×	`fma-udef`

Counts

4 → 187

Calls

4 calls:

0.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
8.0ms	(/ 2.0 (pow x 3))
4.0ms	(/ 1 (pow x 7))
4.0ms	(/ 1 (pow x 5))

series201.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
35.0ms	(/ 2.0 (pow x 3))
57.0ms	(/ 1 (pow x 7))
42.0ms	(/ 1 (pow x 5))

simplify52.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	460	949
1	2326	816
2	5001	816

prune395.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 2.0 (* x x)) x)
0.2b	(/ 1 (pow x 7))
0.3b	(/ 1 (pow x 5))
0.4b	(/ 2.0 (* x x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
19×	`div-exp`
18×	`associate-/r*`
16×	`associate-/l*`
9×	`cbrt-undiv`
8×	`div-inv` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`pow-flip` `prod-exp` `cbrt-unprod` `inv-pow`
1×	`associate-/l/`

Counts

4 → 183

Calls

4 calls:

6.0ms	(/ (/ 2.0 (* x x)) x)
4.0ms	(/ 1 (pow x 7))
4.0ms	(/ 1 (pow x 5))
3.0ms	(/ 2.0 (* x x))

series164.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (/ 2.0 (* x x)) x)
58.0ms	(/ 1 (pow x 7))
41.0ms	(/ 1 (pow x 5))
30.0ms	(/ 2.0 (* x x))

simplify61.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	511	914
1	2528	828
2	5001	768

prune405.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 25.0b

bsearch109.0ms

Steps

Iters	Range		Point
10	2.30341956868392e-10	214.50772926448735	100.54319276910603
9	-1898619.482837422	-0.12347723982223391	-98.70299588451333

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	31
1	39	31

end0.0ms

sample611.0ms

Algorithm

intervals

Results

206.0ms	1868×	body	640	valid
126.0ms	4177×	body	80	valid
83.0ms	567×	body	1280	valid
73.0ms	896×	body	320	valid
27.0ms	492×	body	160	valid