Details

sample66.0ms

Algorithm

intervals

Results

21.0ms	409×	body	80	nan
21.0ms	389×	body	80	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (19.0ms)

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: 4.9b

Counts

2 → 2

localize16.0ms

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)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

122×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
52×	`associate-l`
44×	`add-cube-cbrt`
39×	`prod-diff`
30×	`distribute-lft-out`
24×	`times-frac`
18×	`distribute-lft-out--`
15×	`associate-r`
13×	`fma-neg`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
7×	`unswap-sqr`
6×	`pow1` `add-log-exp`
5×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r*`
2×	`flip3--` `associate-*l/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `fma-udef` `div-inv`

Counts

4 → 159

Calls

4 calls:

16.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
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)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series272.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
122.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
38.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	535	1560
1	1800	1221
2	5002	1177

prune417.0ms

Filtered

171 candidates to 90 candidates (52.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	161	10	171
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	162	11	173

Merged error: 4.0b

Counts

173 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

132×	`*-un-lft-identity`
84×	`add-sqr-sqrt`
61×	`associate-l`
52×	`add-cube-cbrt`
45×	`prod-diff`
25×	`distribute-lft-out`
24×	`times-frac` `distribute-lft-out--`
23×	`associate-r`
15×	`fma-neg`
13×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`difference-of-squares`
8×	`associate-/l*` `unswap-sqr`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `*-commutative` `add-log-exp`
5×	`log-pow`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`flip3--` `associate-/r*` `flip--`
2×	`pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 194

Calls

4 calls:

14.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
15.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series790.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
411.0ms	(- (* (- x 0.5) (log x)) x)
255.0ms	(* (- x 0.5) (log x))
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify89.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	654	1780
1	2421	1391
2	5001	1334

prune522.0ms

Filtered

206 candidates to 109 candidates (52.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	205	12	217

Merged error: 4.0b

Counts

217 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
24×	`times-frac` `associate-l` `distribute-lft-out`
20×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out--`
9×	`cbrt-prod`
8×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 90

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
28.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series630.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
181.0ms	(cbrt x)
185.0ms	(cbrt x)
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify125.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	223	644
1	699	591
2	3468	572
3	5001	565

prune440.0ms

Filtered

102 candidates to 72 candidates (70.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 4.0b

Counts

114 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467))
0.1b	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
4.6b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

348×	`*-un-lft-identity`
247×	`add-sqr-sqrt`
154×	`prod-diff`
132×	`associate-l`
121×	`add-cube-cbrt`
94×	`associate-r`
80×	`distribute-lft-out--`
79×	`times-frac`
64×	`frac-sub`
55×	`distribute-lft-out`
54×	`frac-times`
35×	`difference-of-squares`
34×	`flip3--` `flip--`
30×	`flip3-+` `flip-+` `associate-/l*`
29×	`fma-neg`
27×	`associate-r/` `associate-/r`
26×	`unswap-sqr`
15×	`add-exp-log`
12×	`clear-num`
11×	`add-cbrt-cube` `associate--r+`
9×	`frac-2neg` `un-div-inv` `add-log-exp`
8×	`pow1` `associate-l/` `-commutative`
7×	`div-inv`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log` `cbrt-unprod`
2×	`sub-neg` `div-exp` `pow-prod-down`
1×	`cbrt-undiv` `rec-exp` `1-exp` `fma-udef` `associate--r-`

Counts

4 → 393

Calls

4 calls:

57.0ms	(- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467))
1.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
14.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
30.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series331.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467))
124.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
38.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
86.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify127.0ms

Algorithm

egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2191	8058
1	5003	6850

prune1.0s

Filtered

405 candidates to 190 candidates (46.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	401	4	405
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	408	9	417

Merged error: 3.4b

Counts

417 → 9

regimes287.0ms

Accuracy

0% (2.7b remaining)

Error of 5.9b against oracle of 3.2b and baseline of 5.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample1.7s

Algorithm

intervals

Results

635.0ms	11618×	body	80	valid
543.0ms	11724×	body	80	nan