Details

sample65.0ms

Algorithm

intervals

Results

21.0ms	387×	body	80	valid
19.0ms	420×	body	80	nan

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	12
1	84	12
2	245	12
3	581	12
4	1280	12
5	2462	12
6	5001	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

31.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(* (- x 0.5) (log x))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

443.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
416.0ms	(- (* (- x 0.5) (log x)) x)
253.0ms	(* (- x 0.5) (log x))
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	501	839
1	1642	776
2	5002	763

prune392.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

17.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

789.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
184.0ms	(cbrt x)
177.0ms	(cbrt x)
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify72.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	624	1080
1	2446	943
2	5001	919

prune614.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (log (pow x 1/3)) (- (* 3 x) 1.5)) x)
0.3b	(* (log (pow x 1/3)) (- (* 3 x) 1.5))
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.0b	(pow x 1/3)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `associate--l+`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `associate-/r` `associate-/l`
2×	`flip3--` `associate-*r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `diff-log` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

8.0ms	(- (* (log (pow x 1/3)) (- (* 3 x) 1.5)) x)
11.0ms	(* (log (pow x 1/3)) (- (* 3 x) 1.5))
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
1.0ms	(pow x 1/3)

series1.5s

Counts

4 → 12

Calls

4 calls:

782.0ms	(- (* (log (pow x 1/3)) (- (* 3 x) 1.5)) x)
459.0ms	(* (log (pow x 1/3)) (- (* 3 x) 1.5))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
173.0ms	(pow x 1/3)

simplify58.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	470	779
1	1948	708
2	5001	693

prune376.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1.5 (log (pow (/ 1 x) -1/3)))
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.0b	(pow (/ 1 x) -1/3)
5.0b	(pow (/ 1 x) -1/3)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

52×	`unpow-prod-down`
48×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
45×	`times-frac`
34×	`log-prod`
18×	`add-exp-log`
17×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1`
8×	`pow-exp` `add-cbrt-cube`
6×	`pow-unpow` `pow-pow`
5×	`div-exp` `div-inv`
4×	`associate-r` `add-log-exp` `sqr-pow`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `associate-/l/` `inv-pow`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

10.0ms	(* 1.5 (log (pow (/ 1 x) -1/3)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
4.0ms	(pow (/ 1 x) -1/3)
4.0ms	(pow (/ 1 x) -1/3)

series908.0ms

Counts

4 → 12

Calls

4 calls:

460.0ms	(* 1.5 (log (pow (/ 1 x) -1/3)))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
177.0ms	(pow (/ 1 x) -1/3)
186.0ms	(pow (/ 1 x) -1/3)

simplify68.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	527	1136
1	2092	1001
2	5001	938

prune564.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes287.0ms

Accuracy

72% (0.4b remaining)

Error of 5.2b against oracle of 4.8b and baseline of 6.2b

bsearch43.0ms

Steps

Iters	Range		Point
4	7.008645764064249e+128	1.0678928114084983e+129	9.417268556265354e+128

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	36
1	67	36

end0.0ms

sample1.7s

Algorithm

intervals

Results

635.0ms	11788×	body	80	valid
546.0ms	11982×	body	80	nan