Details

sample63.0ms

Algorithm

intervals

Results

21.0ms	421×	body	80	nan
19.0ms	364×	body	80	valid

simplify57.0ms

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: 7.4b

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)
0.2b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
6.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite29.0ms

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:

7.0ms	(* (+ 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)))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series274.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (+ y 0.0007936500793651) z)
38.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
122.0ms	(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

prune355.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 6.0b

Counts

100 → 8

localize16.0ms

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))
0.2b	(- (* (- x 0.5) (log x)) x)
6.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `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` `fma-neg` `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 → 116

Calls

4 calls:

11.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
7.0ms	(- (* (- x 0.5) (log x)) x)
14.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

429.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
258.0ms	(* (- x 0.5) (log x))
417.0ms	(- (* (- x 0.5) (log x)) x)
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify69.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	576	925
1	2275	825
2	5001	802

prune428.0ms

Filtered

128 candidates to 102 candidates (79.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 5.9b

Counts

136 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.8b	(/ (+ (* (- (* (+ 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` `expm1-log1p-u` `log1p-expm1-u` `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 → 70

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)

series664.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
221.0ms	(cbrt x)
183.0ms	(cbrt x)
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify107.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	223	484
1	699	441
2	3468	432
3	5001	425

prune400.0ms

Filtered

82 candidates to 72 candidates (87.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Merged error: 5.9b

Counts

90 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log x) (- x 0.5) (- (* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))) (- x 0.91893853320467)))
0.2b	(/ 1 (sqrt x))
3.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
4.2b	(* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
94×	`times-frac`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+` `fma-udef` `inv-pow`

Counts

4 → 185

Calls

4 calls:

1.0ms	(fma (log x) (- x 0.5) (- (* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))) (- x 0.91893853320467)))
4.0ms	(/ 1 (sqrt x))
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
23.0ms	(* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(fma (log x) (- x 0.5) (- (* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))) (- x 0.91893853320467)))
32.0ms	(/ 1 (sqrt x))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x))
88.0ms	(* (/ 1 (sqrt x)) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (sqrt x)))

simplify103.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	760	2321
1	4178	2033
2	5002	1974

prune620.0ms

Filtered

197 candidates to 126 candidates (64.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	197	8	205

Merged error: 5.9b

Counts

205 → 8

regimes329.0ms

Accuracy

86.2% (0.3b remaining)

Error of 4.4b against oracle of 4.1b and baseline of 6.2b

bsearch53.0ms

Steps

Iters	Range		Point
6	1.11049414308367e+15	5323393280142883.0	4485947120969833.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	29
1	47	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

591.0ms	11627×	body	80	valid
526.0ms	11619×	body	80	nan