Details

sample118.0ms

Algorithm

intervals

Results

38.0ms	53×	body	1280	valid
17.0ms	40×	body	640	valid
12.0ms	122×	body	80	valid
8.0ms	5×	body	2560	valid
7.0ms	25×	body	320	valid
5.0ms	85×	body	80	nan
3.0ms	45×	body	80	overflowed
3.0ms	9×	body	640	nan
2.0ms	4×	body	1280	nan
2.0ms	12×	body	160	valid
1.0ms	3×	body	320	nan
1.0ms	4×	body	160	nan

simplify235.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	33	7
2	49	7
3	71	7
4	93	7
5	180	7
6	232	7
7	411	7
8	710	7
9	1092	7
10	1240	7
11	1558	7
12	4191	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.1b	(log (+ (- 1.0 y) (* y (exp z))))
2.6b	(+ (- 1.0 y) (* y (exp z)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* y (exp z))
23.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
13.0ms	(+ (- 1.0 y) (* y (exp z)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* y (exp z))
179.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
79.0ms	(log (+ (- 1.0 y) (* y (exp z))))
44.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	452	795
1	1740	733
2	5001	726

prune322.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow z 2))
0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
3.8b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
8.5b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-r`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-l` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

6.0ms	(* 0.5 (pow z 2))
3.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
11.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
11.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

series345.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 0.5 (pow z 2))
79.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
98.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
140.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify70.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	415	806
1	1836	721
2	5001	715

prune375.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow z 2))
0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
3.8b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
8.6b	(* (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (/ 1 t))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-exp-log`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
9×	`associate-l`
8×	`pow1` `prod-exp` `unswap-sqr`
6×	`add-log-exp`
4×	`unpow-prod-down` `flip3-+` `cbrt-unprod` `flip-+`
3×	`associate-r/` `-commutative`
2×	`frac-times` `div-exp` `pow-prod-down` `associate-*l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rec-exp` `distribute-lft-in` `1-exp` `pow-exp` `sum-log` `un-div-inv` `div-inv`

Counts

4 → 100

Calls

4 calls:

5.0ms	(* 0.5 (pow z 2))
3.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
11.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
14.0ms	(* (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (/ 1 t))

series343.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 0.5 (pow z 2))
77.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
98.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
141.0ms	(* (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) (/ 1 t))

simplify87.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	526	909
1	2623	809
2	5001	797

prune405.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
0.4b	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
3.8b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
8.4b	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
60×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp`
7×	`pow1` `flip3-+` `flip-+`
6×	`div-inv` `associate-/l*` `add-log-exp`
4×	`cbrt-undiv`
3×	`associate-r` `associate-l`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `pow-flip` `distribute-lft-in` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

3.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
9.0ms	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
15.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.0ms	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

series623.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
175.0ms	(/ 1 (/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z))))))
97.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
274.0ms	(/ t (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	649	2208
1	3269	2018
2	5001	1932

prune428.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.6b

regimes781.0ms

Accuracy

72.5% (4.5b remaining)

Error of 9.1b against oracle of 4.6b and baseline of 21.0b

bsearch171.0ms

Steps

Iters	Range		Point
8	5.372578135583532e-175	4.22161995161178e-172	1.542824074531081e-172
6	-1.0593086886337258e-08	-1.856415563400247e-09	-3.016368863520559e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	26
1	54	26

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.0s	1432×	body	1280	valid
698.0ms	1657×	body	640	valid
323.0ms	3477×	body	80	valid
249.0ms	899×	body	320	valid
164.0ms	2529×	body	80	nan
137.0ms	89×	body	2560	valid
110.0ms	1544×	body	80	overflowed
99.0ms	306×	body	640	nan
92.0ms	482×	body	160	valid
52.0ms	117×	body	1280	nan
48.0ms	181×	body	320	nan
17.0ms	116×	body	160	nan