Details

sample18.0ms

Algorithm

intervals

Results

4.0ms	192×	body	80	valid
2.0ms	26×	body	640	valid
1.0ms	11×	body	1280	valid
1.0ms	17×	body	320	valid
0.0ms	10×	body	160	valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (10.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize6.0ms

Local error

Found 1 expressions with local error:

3.0b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (17.0ms)

Iter	Nodes	Cost
0	59	83
1	163	71
2	523	68
3	1872	66
4	5001	66

prune38.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.0b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.9b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `prod-diff`
24×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
5×	`pow1` `associate-l` `distribute-lft-out` `add-log-exp`
4×	`flip3-+` `associate-l/` `associate-/r` `flip-+` `div-inv`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-r` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `unswap-sqr`

Counts

3 → 102

Calls

3 calls:

22.0ms	(* (- 1.0 x) y)
22.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
22.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series123.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* (- 1.0 x) y)
60.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
37.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	532	1321
1	2345	955
2	5002	952

prune195.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.1b	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
4.5b	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
20.2b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
39×	`prod-diff`
37×	`add-cube-cbrt`
22×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
20×	`add-exp-log` `add-cbrt-cube`
15×	`associate-l`
8×	`pow1` `times-frac` `associate-r`
7×	`flip3--` `flip--`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`sub-neg` `associate-*l/` `difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`fma-neg`
2×	`frac-times` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `associate-/l/` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l*`

Counts

4 → 155

Calls

4 calls:

20.0ms	(* (- 1.0 x) y)
69.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
9.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
27.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (- 1.0 x) y)
71.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
142.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
82.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify127.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	782	1913
1	4408	1574
2	5001	1565

prune310.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (* 1.0 (/ x y)))
0.0b	(+ (/ 1.0 y) (- x (* 1.0 (/ x y))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`fma-def`
12×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac` `add-log-exp`
6×	`prod-diff`
5×	`associate-+r+`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `frac-add` `sum-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+` `div-inv` `distribute-lft-out`

Counts

2 → 56

Calls

2 calls:

6.0ms	(- x (* 1.0 (/ x y)))
26.0ms	(+ (/ 1.0 y) (- x (* 1.0 (/ x y))))

series55.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(- x (* 1.0 (/ x y)))
26.0ms	(+ (/ 1.0 y) (- x (* 1.0 (/ x y))))

simplify111.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	234	339
1	742	307
2	4339	290
3	5001	290

prune119.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes79.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.2b

bsearch71.0ms

Steps

Iters	Range		Point
10	0.005224711248419297	463191646.4289385	167881476.73563808
9	-31625873581007.836	-12786724.3536924	-172408127.57777166

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	9
1	24	9

end0.0ms

sample498.0ms

Algorithm

intervals

Results

150.0ms	6125×	body	80	valid
67.0ms	707×	body	640	valid
44.0ms	405×	body	1280	valid
34.0ms	482×	body	320	valid
12.0ms	281×	body	160	valid