Details

sample58.0ms

Algorithm

intervals

Results

19.0ms	374×	body	80	valid
17.0ms	373×	body	80	nan

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (18.0ms)

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.4b

localize20.0ms

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)))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite29.0ms

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)
9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series270.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
42.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
120.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (43.0ms)

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

prune346.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

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)))
0.1b	(* (log x) (- x 0.5))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite67.0ms

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:

8.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
30.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
7.0ms	(* (log x) (- x 0.5))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series510.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (- (* (+ 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)))
255.0ms	(* (log x) (- x 0.5))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify142.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (27.0ms)

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

prune807.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.0b

localize22.0ms

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)))
5.2b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite33.0ms

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:

6.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
15.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series454.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
41.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
121.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
269.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify67.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (56.0ms)

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

prune388.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.4b	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
0.4b	(* (log x) (+ (sqrt x) (sqrt 0.5)))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

209×	`prod-diff`
195×	`add-sqr-sqrt`
193×	`*-un-lft-identity`
159×	`add-cube-cbrt`
152×	`sqrt-prod`
77×	`distribute-rgt-in` `distribute-lft-in`
76×	`associate-+l+`
68×	`associate-+r+`
54×	`times-frac`
42×	`associate-*r/`
32×	`frac-add`
31×	`flip3--` `flip--`
20×	`frac-times`
18×	`flip3-+` `flip-+`
17×	`difference-of-squares`
16×	`frac-sub`
15×	`distribute-lft-out--`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
12×	`pow1`
10×	`associate-*l/`
6×	`div-inv`
5×	`sub-neg` `associate-l`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`diff-log` `associate-/r` `sum-log` `associate-/l`
2×	`*-commutative` `associate-/l/` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `fma-def` `frac-2neg` `div-exp` `clear-num` `log-pow` `associate--r-` `unswap-sqr`

Counts

4 → 361

Calls

4 calls:

45.0ms	(+ (* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
17.0ms	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
8.0ms	(* (log x) (+ (sqrt x) (sqrt 0.5)))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series748.0ms

Counts

4 → 12

Calls

4 calls:

381.0ms	(+ (* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5))) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
201.0ms	(* (* (log x) (+ (sqrt x) (sqrt 0.5))) (- (sqrt x) (sqrt 0.5)))
74.0ms	(* (log x) (+ (sqrt x) (sqrt 0.5)))
90.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify123.0ms

Algorithm

egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2369	9697
1	5003	8331

prune1.5s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.0b

regimes408.0ms

Accuracy

75.9% (0.5b remaining)

Error of 4.5b against oracle of 3.9b and baseline of 6.2b

bsearch81.0ms

Steps

Iters	Range		Point
9	1.1057521050711306e+85	7.491092794297452e+92	1.9602415927594686e+85

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	22
1	42	22

end0.0ms

sample1.7s

Algorithm

intervals

Results

618.0ms	11804×	body	80	valid
535.0ms	11753×	body	80	nan