Details

analyze459.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

sample34.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
2.0ms	34×	body	80	invalid
2.0ms	26×	body	80	nan

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5068	24

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 5.8b

Counts

2 → 1

localize20.0ms

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)
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite38.0ms

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` `add-cbrt-cube`
7×	`pow1` `associate-+l+`
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 → 96

Calls

4 calls:

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

series113.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
21.0ms	(* (- x 0.5) (log x))
37.0ms	(- (* (- x 0.5) (log x)) x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify64.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4955	1424
1	4955	1424

prune260.0ms

Filtered

88 candidates to 108 candidates (-22.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	96	12	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 0.0b

Counts

109 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (- x 0.5) (log (sqrt x))) (- (* (- x 0.5) (log (sqrt x))) x))
0.2b	(* (- x 0.5) (log (sqrt x)))
0.2b	(* (- x 0.5) (log (sqrt x)))
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

16.0ms	(+ (* (- x 0.5) (log (sqrt x))) (- (* (- x 0.5) (log (sqrt x))) x))
8.0ms	(* (- x 0.5) (log (sqrt x)))
8.0ms	(* (- x 0.5) (log (sqrt x)))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series48.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (* (- x 0.5) (log (sqrt x))) (- (* (- x 0.5) (log (sqrt x))) x))
7.0ms	(* (- x 0.5) (log (sqrt x)))
7.0ms	(* (- x 0.5) (log (sqrt x)))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4918	2382
1	4918	2382

prune300.0ms

Filtered

109 candidates to 157 candidates (-44.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Merged error: 0.0b

Counts

169 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log (sqrt (sqrt x))))
0.2b	(- (* (- x 0.5) (log (sqrt (sqrt x)))) x)
0.3b	(+ (log (sqrt x)) (log (sqrt (sqrt x))))
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

51×	`log-prod`
48×	`sqrt-prod`
39×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
29×	`log-pow`
24×	`pow1`
18×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
17×	`sqrt-pow1`
11×	`pow1/2`
9×	`associate-+r+` `times-frac`
8×	`add-exp-log` `distribute-rgt-out` `associate-r` `add-cbrt-cube`
6×	`associate-+l+` `distribute-lft-out` `add-log-exp`
5×	`associate-l`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-*l/` `distribute-rgt1-in` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

9.0ms	(* (- x 0.5) (log (sqrt (sqrt x))))
9.0ms	(- (* (- x 0.5) (log (sqrt (sqrt x)))) x)
10.0ms	(+ (log (sqrt x)) (log (sqrt (sqrt x))))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series139.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (- x 0.5) (log (sqrt (sqrt x))))
70.0ms	(- (* (- x 0.5) (log (sqrt (sqrt x)))) x)
10.0ms	(+ (log (sqrt x)) (log (sqrt (sqrt x))))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4990	1986
1	4990	1986

prune293.0ms

Filtered

107 candidates to 157 candidates (-46.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	157	10	167

Merged error: 0.0b

Counts

167 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (- x 0.5) (log (sqrt (sqrt x)))) x)
0.2b	(* z (/ 0.0027777777777778 x))
0.3b	(+ (log (sqrt x)) (log (sqrt (sqrt x))))
0.4b	(* 0.0007936500793651 (* z (/ z x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

33×	`log-prod`
30×	`*-un-lft-identity` `sqrt-prod`
29×	`add-sqr-sqrt`
26×	`pow1`
24×	`add-cube-cbrt` `log-pow`
18×	`add-exp-log` `associate--l+` `add-cbrt-cube`
14×	`associate-r`
13×	`sqrt-pow1`
10×	`times-frac`
9×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow1/2`
8×	`distribute-rgt-out`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-+l+` `associate-l` `distribute-lft-out` `add-log-exp`
4×	`pow-prod-down`
3×	`associate-*r/`
2×	`cbrt-undiv` `div-exp` `distribute-rgt1-in` `*-commutative` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+` `div-inv`

Counts

4 → 124

Calls

4 calls:

9.0ms	(- (* (- x 0.5) (log (sqrt (sqrt x)))) x)
6.0ms	(* z (/ 0.0027777777777778 x))
8.0ms	(+ (log (sqrt x)) (log (sqrt (sqrt x))))
6.0ms	(* 0.0007936500793651 (* z (/ z x)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* (- x 0.5) (log (sqrt (sqrt x)))) x)
3.0ms	(* z (/ 0.0027777777777778 x))
10.0ms	(+ (log (sqrt x)) (log (sqrt (sqrt x))))
4.0ms	(* 0.0007936500793651 (* z (/ z x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4942	1210
1	4942	1210

prune198.0ms

Filtered

89 candidates to 136 candidates (-52.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Merged error: 0.0b

Counts

146 → 11

regimes733.0ms

Accuracy

89.5% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 6.4b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	241	94
1	241	94

end0.0ms

sample933.0ms

Algorithm

intervals

Results

558.0ms	8000×	body	80	valid
86.0ms	1242×	body	80	invalid
47.0ms	766×	body	80	nan

Details

analyze459.0ms

sample34.0ms

simplify42.0ms

prune8.0ms

localize20.0ms

rewrite38.0ms

series113.0ms

simplify64.0ms

prune260.0ms

localize20.0ms

rewrite51.0ms

series48.0ms

simplify63.0ms

prune300.0ms

localize25.0ms

rewrite45.0ms

series139.0ms

simplify58.0ms

prune293.0ms

localize28.0ms

rewrite34.0ms

series88.0ms

simplify74.0ms

prune198.0ms

regimes733.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample933.0ms

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