Details

sample63.0ms

Algorithm

intervals

Results

20.0ms	398×	body	80	valid
18.0ms	424×	body	80	nan

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (16.0ms)

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite48.0ms

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:

6.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series268.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
120.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
41.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify49.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (39.0ms)

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

prune342.0ms

Filtered

93 candidates to 73 candidates (78.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize16.0ms

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))
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite200.0ms

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)
133.0ms	(+ (* (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)

series521.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- (* (+ 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)))
262.0ms	(* (log x) (- x 0.5))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify134.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (26.0ms)

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

prune778.0ms

Filtered

227 candidates to 155 candidates (68.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b	(+ (* (log x) (- x 0.5)) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
0.2b	(* (log x) (- x 0.5))
6.2b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 201

Calls

4 calls:

0.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
54.0ms	(+ (* (log x) (- x 0.5)) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
12.0ms	(* (log x) (- x 0.5))
2.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series566.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
168.0ms	(+ (* (log x) (- x 0.5)) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
281.0ms	(* (log x) (- x 0.5))
76.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify120.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1130	3190
1	4346	2778
2	5001	2778

prune778.0ms

Filtered

213 candidates to 147 candidates (69.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log x) (- x 0.5))
0.2b	(* (log x) (- x 0.5))
0.5b	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
6.2b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

59×	`pow1`
54×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`prod-diff`
28×	`sqrt-pow1`
22×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
18×	`associate-*r/`
14×	`associate-r`
12×	`add-exp-log` `sqrt-div` `associate-l` `add-cbrt-cube`
10×	`pow1/2` `pow-prod-up`
9×	`times-frac`
8×	`flip3--` `flip--`
6×	`pow-sqr`
4×	`expm1-log1p-u` `frac-times` `sub-neg` `swap-sqr` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`associate-*l/` `log-pow` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `clear-num` `rem-square-sqrt` `div-inv`

Counts

4 → 182

Calls

4 calls:

12.0ms	(* (log x) (- x 0.5))
12.0ms	(* (log x) (- x 0.5))
30.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
2.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series848.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (log x) (- x 0.5))
259.0ms	(* (log x) (- x 0.5))
241.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
79.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify99.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	777	1696
1	3264	1330
2	5001	1303

prune542.0ms

Filtered

194 candidates to 101 candidates (52.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

regimes394.0ms

Accuracy

88.4% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 5.9b

bsearch100.0ms

Steps

Iters	Range		Point
9	4599562040646.685	1.3528688105735311e+18	2777690040622108.0

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample1.7s

Algorithm

intervals

Results

607.0ms	11689×	body	80	valid
533.0ms	11704×	body	80	nan