Details

sample9.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize4.0ms

Local error

Found 1 expressions with local error:

12.0b

(/ x (+ (* x x) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

6.0ms

(/ x (+ (* x x) 1.0))

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

(/ x (+ (* x x) 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	171	215
1	589	196
2	1979	191
3	5002	186

prune69.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

2.3b	(/ x (fma (- 1.0) 1.0 (pow x 4)))
15.7b	(* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- (* x x) 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-l`
9×	`add-exp-log` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`pow1` `associate-r`
3×	`associate-/r` `associate-/l`
2×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `sub-neg` `flip3--` `associate-*r/` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `difference-of-squares`

Counts

2 → 78

Calls

2 calls:

2.0ms	(/ x (fma (- 1.0) 1.0 (pow x 4)))
17.0ms	(* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- (* x x) 1.0))

series277.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(/ x (fma (- 1.0) 1.0 (pow x 4)))
114.0ms	(* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- (* x x) 1.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	446	816
1	2125	716
2	5001	706

prune188.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ (pow x 3) (fma (- 1.0) 1.0 (pow x 4))) (* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- 1.0)))
2.3b	(/ x (fma (- 1.0) 1.0 (pow x 4)))
18.3b	(/ (pow x 3) (fma (- 1.0) 1.0 (pow x 4)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
40×	`fma-def`
21×	`unpow-prod-down` `cube-prod`
15×	`associate-/l*`
10×	`add-exp-log`
7×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `distribute-rgt-neg-out`
1×	`+-commutative` `pow-to-exp` `flip3-+` `unsub-neg` `associate-*l/` `frac-add` `pow-exp` `sum-log` `flip-+`

Counts

3 → 152

Calls

3 calls:

25.0ms	(+ (/ (pow x 3) (fma (- 1.0) 1.0 (pow x 4))) (* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- 1.0)))
5.0ms	(/ x (fma (- 1.0) 1.0 (pow x 4)))
5.0ms	(/ (pow x 3) (fma (- 1.0) 1.0 (pow x 4)))

series470.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(+ (/ (pow x 3) (fma (- 1.0) 1.0 (pow x 4))) (* (/ x (fma (- 1.0) 1.0 (pow x 4))) (- 1.0)))
162.0ms	(/ x (fma (- 1.0) 1.0 (pow x 4)))
178.0ms	(/ (pow x 3) (fma (- 1.0) 1.0 (pow x 4)))

simplify69.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	446	1166
1	2085	1101
2	5001	1098

prune404.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (pow x 9))
0.3b	(/ 1 (pow x 5))
2.3b	(/ x (fma (- 1.0) 1.0 (pow x 4)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
43×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
23×	`add-exp-log`
17×	`associate-/r*`
13×	`div-exp`
9×	`add-cbrt-cube` `associate-/l*`
8×	`sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `inv-pow`

Counts

3 → 139

Calls

3 calls:

4.0ms	(/ 1 (pow x 9))
4.0ms	(/ 1 (pow x 5))
2.0ms	(/ x (fma (- 1.0) 1.0 (pow x 4)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ 1 (pow x 9))
49.0ms	(/ 1 (pow x 5))
168.0ms	(/ x (fma (- 1.0) 1.0 (pow x 4)))

simplify42.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	396	767
1	1768	705
2	5001	644

prune359.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 23.3b

bsearch79.0ms

Steps

Iters	Range		Point
10	2.30341956868392e-10	214.50772926448735	19.9196551064146
9	-1898619.482837422	-0.12347723982223391	-3787.269001220626

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	42	21
2	45	21
3	45	21

end0.0ms

sample224.0ms

Algorithm

intervals

Results

142.0ms

8000×

body

valid