Details

sample67.0ms

Algorithm

intervals

Results

23.0ms	384×	body	80	valid
20.0ms	425×	body	80	nan

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 6.1b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ y 0.0007936500793651) z)
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)))
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (+ y 0.0007936500793651) z)
8.0ms	(* (- (* (+ 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)))
14.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series268.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (+ y 0.0007936500793651) z)
36.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
118.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	446	778
1	1546	696
2	5002	694

prune519.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 4.5b

Counts

100 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(+ (* (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))
5.7b	(/ (+ (* (- (* (+ 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:

9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
28.0ms	(+ (* (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))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series506.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
134.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
244.0ms	(* (log x) (- x 0.5))
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify141.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (29.0ms)

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

prune696.0ms

Filtered

227 candidates to 155 candidates (68.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	222	5	227
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	223	12	235

Merged error: 4.4b

Counts

235 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

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) (sqrt x)) (sqrt x)) (- x 0.91893853320467)))
3.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
3.1b	(/ (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)) (sqrt x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`add-cube-cbrt` `*-un-lft-identity`
144×	`sqrt-prod`
25×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/l/`
2×	`frac-2neg` `associate-*l/` `clear-num`
1×	`flip3--` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `unswap-sqr`

Counts

4 → 252

Calls

4 calls:

13.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)) (sqrt x)) (- x 0.91893853320467)))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
16.0ms	(/ (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)) (sqrt x))

series359.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
151.0ms	(fma (log x) (- x 0.5) (- (/ (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)) (sqrt x)) (- x 0.91893853320467)))
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
80.0ms	(/ (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)) (sqrt x))

simplify100.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	866	4342
1	3183	3940
2	5002	3913

prune640.0ms

Filtered

264 candidates to 141 candidates (53.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	265	11	276

Merged error: 4.4b

Counts

276 → 11

localize20.0ms

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))))
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite52.0ms

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` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `div-exp` `clear-num` `rem-square-sqrt` `flip-+` `div-inv`

Counts

4 → 184

Calls

4 calls:

11.0ms	(* (log x) (- x 0.5))
8.0ms	(* (log x) (- x 0.5))
14.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series822.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(* (log x) (- x 0.5))
254.0ms	(* (log x) (- x 0.5))
232.0ms	(* (sqrt (* (log x) (- x 0.5))) (sqrt (* (log x) (- x 0.5))))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify112.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	830	1757
1	3483	1389
2	5003	1358

prune471.0ms

Filtered

196 candidates to 104 candidates (53.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	195	12	207

Merged error: 4.4b

Counts

207 → 12

regimes453.0ms

Accuracy

86.3% (0.3b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 5.8b

bsearch77.0ms

Steps

Iters	Range		Point
8	6244423733497697.0	5.188476466533857e+18	2.1113340483712486e+17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	28
1	44	28

end0.0ms

sample1.7s

Algorithm

intervals

Results

624.0ms	11675×	body	80	valid
553.0ms	11641×	body	80	nan