Details

sample86.0ms

Algorithm

intervals

Results

26.0ms	380×	body	80	nan
24.0ms	365×	body	80	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	12
1	84	12
2	245	12
3	581	12
4	1280	12
5	2462	12
6	5001	12

prune5.0ms

Filtered

1 candidates to 0 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: 6.0b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
6.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series113.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
33.0ms	(- (* (- x 0.5) (log x)) x)
21.0ms	(* (- x 0.5) (log x))
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	543	875
1	1816	820
2	5001	763

prune759.0ms

Filtered

110 candidates to 83 candidates (24.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	12	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Merged error: 4.4b

Counts

111 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series88.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
25.0ms	(cbrt x)
21.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify93.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	231	498
1	697	460
2	3102	429
3	5001	426

prune569.0ms

Filtered

74 candidates to 59 candidates (20.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	74	12	86

Merged error: 4.4b

Counts

86 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
0.3b	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
5.5b	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
66×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
62×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
12×	`log-prod`
11×	`associate-/r/`
8×	`pow1` `div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `div-inv` `associate-/l*` `add-log-exp`
5×	`flip3-+` `associate-l` `flip-+`
4×	`cbrt-undiv` `associate-r`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `flip--`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 160

Calls

4 calls:

6.0ms	(- (* (- x 0.5) (log x)) x)
9.0ms	(* (- x 0.5) (log x))
13.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
11.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

series120.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* (- x 0.5) (log x)) x)
23.0ms	(* (- x 0.5) (log x))
25.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
38.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

simplify85.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	744	1921
1	3238	1766
2	5003	1666

prune1.1s

Filtered

172 candidates to 101 candidates (41.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	171	13	184

Merged error: 3.6b

Counts

184 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
5.8b	(/ (/ 1 x) (/ 1 (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

465×	`times-frac`
226×	`add-sqr-sqrt` `*-un-lft-identity`
222×	`add-cube-cbrt`
46×	`add-exp-log`
32×	`div-exp`
31×	`div-inv`
29×	`associate-/r/`
18×	`log-prod` `add-cbrt-cube`
15×	`flip3-+` `associate-/r*` `flip-+`
13×	`associate-/l*`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in`
8×	`cbrt-undiv` `rec-exp` `associate-+l+` `1-exp`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
2×	`sub-neg` `flip3--` `diff-log` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `associate-+l-` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 324

Calls

4 calls:

10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))
19.0ms	(/ (/ 1 x) (/ 1 (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
37.0ms	(- (* (- x 0.5) (log x)) x)
20.0ms	(* (- x 0.5) (log x))
26.0ms	(/ (/ 1 x) (/ 1 (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))

simplify90.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1719	5362
1	5001	4916

prune2.7s

Filtered

336 candidates to 175 candidates (47.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	337	12	349

Merged error: 2.8b

Counts

349 → 12

regimes664.0ms

Accuracy

75.9% (0.7b remaining)

Error of 3.6b against oracle of 2.8b and baseline of 5.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	36
1	46	36

end0.0ms

sample2.3s

Algorithm

intervals

Results

776.0ms	11658×	body	80	valid
699.0ms	11781×	body	80	nan

Details

sample86.0ms

simplify55.0ms

prune5.0ms

localize17.0ms

rewrite37.0ms

series113.0ms

simplify51.0ms

prune759.0ms

localize27.0ms

rewrite16.0ms

series88.0ms

simplify93.0ms

prune569.0ms

localize18.0ms

rewrite45.0ms

series120.0ms

simplify85.0ms

prune1.1s

localize19.0ms

rewrite63.0ms

series117.0ms

simplify90.0ms

prune2.7s

regimes664.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling