Details

sample56.0ms

Algorithm

intervals

Results

18.0ms	359×	body	80	valid
16.0ms	372×	body	80	nan

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (20.0ms)

Iter	Nodes	Cost
0	40	12
1	92	12
2	269	12
3	669	12
4	1565	11
5	2855	11
6	5001	11

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
4.6b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `prod-diff` `associate-/r` `associate-/l`
2×	`flip3--` `associate-*l/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

5.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series274.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
125.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	432	812
1	1472	709
2	5003	707

prune336.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.2b	(* (log x) (- x 0.5))
4.6b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
116×	`*-un-lft-identity`
101×	`prod-diff`
88×	`add-cube-cbrt`
68×	`associate-+r+`
54×	`times-frac`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`add-log-exp`
10×	`add-exp-log` `flip3--` `associate-*r/` `add-cbrt-cube` `flip--`
9×	`pow1`
8×	`associate-r` `frac-add`
7×	`associate-l`
6×	`div-inv`
5×	`sub-neg`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u`
3×	`diff-log` `associate-/r` `sum-log` `associate-/l`
2×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `fma-def` `frac-2neg` `div-exp` `clear-num` `log-pow` `associate--r-`

Counts

4 → 215

Calls

4 calls:

19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
129.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
12.0ms	(* (log x) (- x 0.5))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series513.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
132.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
252.0ms	(* (log x) (- x 0.5))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify145.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1253	3523
1	4882	3081
2	5001	3081

prune779.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
4.8b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`-un-lft-identity` `associate-r*`
15×	`add-exp-log` `add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `cbrt-unprod`
2×	`frac-times` `flip3--` `flip3-+` `div-exp` `pow-prod-down` `*-commutative` `flip--` `flip-+`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `fma-neg` `diff-log` `1-exp` `associate-*r/` `un-div-inv` `fma-udef` `div-inv`

Counts

4 → 92

Calls

4 calls:

5.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
18.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
40.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series277.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
43.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
124.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
85.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify67.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	541	898
1	2135	771
2	5002	751

prune375.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (fma (sqrt x) (sqrt x) (- (* 0.5 1))) (log x)) (fma (fma (- 0.5) 1 0.5) (log x) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))))
0.2b	(* (fma (sqrt x) (sqrt x) (- (* 0.5 1))) (log x))
0.3b	(fma (sqrt x) (sqrt x) (- (* 0.5 1)))
4.6b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`log-prod`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`flip3-+` `flip-+` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `fma-def` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

4.0ms	(+ (* (fma (sqrt x) (sqrt x) (- (* 0.5 1))) (log x)) (fma (fma (- 0.5) 1 0.5) (log x) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))))
4.0ms	(* (fma (sqrt x) (sqrt x) (- (* 0.5 1))) (log x))
0.0ms	(fma (sqrt x) (sqrt x) (- (* 0.5 1)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series580.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(+ (* (fma (sqrt x) (sqrt x) (- (* 0.5 1))) (log x)) (fma (fma (- 0.5) 1 0.5) (log x) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))))
155.0ms	(* (fma (sqrt x) (sqrt x) (- (* 0.5 1))) (log x))
96.0ms	(fma (sqrt x) (sqrt x) (- (* 0.5 1)))
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	570	1355
1	2120	1196
2	5001	1122

prune488.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.5b

regimes287.0ms

Accuracy

85.8% (0.3b remaining)

Error of 4.3b against oracle of 4.0b and baseline of 6.1b

bsearch82.0ms

Steps

Iters	Range		Point
7	1.7783968927418735e+20	2.9334814637495796e+21	2.1740444753071365e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	39
1	68	39
2	68	39

end0.0ms

sample1.6s

Algorithm

intervals

Results

620.0ms	11689×	body	80	valid
514.0ms	11542×	body	80	nan