Details

sample65.0ms

Algorithm

intervals

Results

23.0ms	381×	body	80	valid
17.0ms	375×	body	80	nan

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (21.0ms)

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

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 5.7b

Counts

2 → 2

localize18.0ms

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)))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
38×	`associate-l`
30×	`add-sqr-sqrt`
26×	`distribute-lft-out`
24×	`times-frac`
21×	`add-cube-cbrt`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/l*`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `unswap-sqr`
2×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `difference-of-squares`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

4 → 111

Calls

4 calls:

6.0ms	(* (+ y 0.0007936500793651) z)
15.0ms	(* (- (* (+ 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)))
28.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series505.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (+ y 0.0007936500793651) z)
47.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
132.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
296.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	451	963
1	1553	881
2	5002	879

prune316.0ms

Filtered

123 candidates to 81 candidates (34.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	116	9	125

Merged error: 3.8b

Counts

125 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

175×	`*-un-lft-identity`
119×	`add-sqr-sqrt`
90×	`prod-diff`
77×	`add-cube-cbrt`
70×	`associate-l`
53×	`associate-+l+`
32×	`associate-r` `distribute-lft-out--`
28×	`distribute-lft-out`
24×	`times-frac`
18×	`log-prod`
15×	`fma-neg`
14×	`pow1`
12×	`associate--l+` `difference-of-squares`
11×	`add-log-exp`
10×	`unswap-sqr`
9×	`distribute-rgt-in` `distribute-lft-in`
8×	`add-exp-log` `fma-def` `log-pow` `-commutative` `add-cbrt-cube` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*`
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` `cbrt-unprod` `div-inv`

Counts

4 → 247

Calls

4 calls:

23.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
15.0ms	(- (* (- x 0.5) (log x)) x)
27.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

453.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
266.0ms	(* (- x 0.5) (log x))
432.0ms	(- (* (- x 0.5) (log x)) x)
94.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify95.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	660	2097
1	2418	1560
2	5001	1487

prune613.0ms

Filtered

259 candidates to 154 candidates (40.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	254	5	259
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	258	10	268

Merged error: 3.7b

Counts

268 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms

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)
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series670.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt x)
194.0ms	(cbrt x)
188.0ms	(cbrt x)
96.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify117.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	223	644
1	699	591
2	3463	572
3	5001	565

prune380.0ms

Filtered

102 candidates to 72 candidates (29.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	102	10	112

Merged error: 3.7b

Counts

112 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

130×	`*-un-lft-identity`
57×	`associate-r`
53×	`add-sqr-sqrt`
52×	`associate-l`
41×	`distribute-lft-out`
40×	`add-cube-cbrt`
36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`fma-def`
24×	`cbrt-prod` `associate-+l+` `times-frac`
19×	`distribute-lft-out--`
13×	`pow1` `distribute-rgt-out`
12×	`associate-+r+` `log-pow`
8×	`associate-l/` `associate-/l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow1/3`
4×	`expm1-log1p-u` `flip3--` `frac-add` `*-commutative` `flip--` `log1p-expm1-u` `unswap-sqr`
3×	`associate-/r*` `difference-of-squares`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 186

Calls

4 calls:

45.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

843.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
189.0ms	(cbrt x)
196.0ms	(cbrt x)
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify120.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	777	1410
1	3619	1195
2	5001	1185

prune702.0ms

Filtered

198 candidates to 146 candidates (26.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	199	9	208

Merged error: 3.7b

Counts

208 → 9

regimes396.0ms

Accuracy

87.8% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 5.8b

bsearch87.0ms

Steps

Iters	Range		Point
7	66699394050389.18	6175297444906509.0	3118050248005774.5

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	23
1	43	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

633.0ms	11690×	body	80	valid
577.0ms	11791×	body	80	nan