Details

analyze670.0ms

Algorithm: search

sample31.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
2.0ms	34×	body	80	invalid
2.0ms	26×	body	80	nan

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

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: 5.0b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite35.0ms

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:

6.0ms	(* (- x 0.5) (log x))
9.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
6.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series110.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (- x 0.5) (log x))
33.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
36.0ms	(- (* (- x 0.5) (log x)) x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (39.0ms)

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

prune217.0ms

Filtered

83 candidates to 110 candidates (-32.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	99	11	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	11	111

Merged error: 3.7b

Counts

111 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
6.0ms	(* (cbrt x) (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)
23.0ms	(cbrt x)
23.0ms	(* (cbrt x) (cbrt x))
20.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	317	643
1	1114	594
2	5002	548

prune177.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 3.7b

Counts

114 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (- x 0.5) (log (pow x 2/3))) (- (* (log (cbrt x)) (- x 0.5)) x))
0.5b	(cbrt x)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
6.0b	(pow x 2/3)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`associate-+l+` `log-prod`
9×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in` `times-frac` `add-log-exp`
7×	`add-exp-log`
6×	`associate-+r+` `add-cbrt-cube`
5×	`pow1`
4×	`flip3--` `associate-*l/` `frac-add` `associate--l+` `flip--`
3×	`cbrt-prod` `sub-neg` `pow-unpow` `associate-/r` `associate-/l` `sqr-pow`
2×	`flip3-+` `sum-log` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `div-inv`

Counts

4 → 94

Calls

4 calls:

14.0ms	(+ (* (- x 0.5) (log (pow x 2/3))) (- (* (log (cbrt x)) (- x 0.5)) x))
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
2.0ms	(pow x 2/3)

series252.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(+ (* (- x 0.5) (log (pow x 2/3))) (- (* (log (cbrt x)) (- x 0.5)) x))
21.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
21.0ms	(pow x 2/3)

simplify78.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	709	1106
1	3059	996
2	5001	950

prune271.0ms

Filtered

83 candidates to 106 candidates (-27.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 3.7b

Counts

117 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (* (- x 0.5) (log (sqrt x))) (- (* (log (sqrt x)) (- x 0.5)) x)) 0.91893853320467)
0.1b	(* (- x 0.5) (log (sqrt x)))
0.1b	(+ (* (- x 0.5) (log (sqrt x))) (- (* (log (sqrt x)) (- x 0.5)) x))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

14.0ms	(+ (+ (* (- x 0.5) (log (sqrt x))) (- (* (log (sqrt x)) (- x 0.5)) x)) 0.91893853320467)
7.0ms	(* (- x 0.5) (log (sqrt x)))
14.0ms	(+ (* (- x 0.5) (log (sqrt x))) (- (* (log (sqrt x)) (- x 0.5)) x))
10.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series55.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (* (- x 0.5) (log (sqrt x))) (- (* (log (sqrt x)) (- x 0.5)) x)) 0.91893853320467)
7.0ms	(* (- x 0.5) (log (sqrt x)))
13.0ms	(+ (* (- x 0.5) (log (sqrt x))) (- (* (log (sqrt x)) (- x 0.5)) x))
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify90.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	870	1565
1	3667	1402
2	5001	1364

prune208.0ms

Filtered

97 candidates to 129 candidates (-33.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	129	11	140

Merged error: 3.6b

Counts

140 → 11

regimes483.0ms

Accuracy

0% (1.3b remaining)

Error of 6.0b against oracle of 4.7b and baseline of 6.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	13
1	32	13

end0.0ms

analyze455.0ms

Algorithm: search

sample884.0ms

Algorithm

intervals

Results

544.0ms	8000×	body	80	valid
82.0ms	1216×	body	80	invalid
44.0ms	728×	body	80	nan

Details

analyze670.0ms

sample31.0ms

simplify50.0ms

prune4.0ms

localize19.0ms

rewrite35.0ms

series110.0ms

simplify51.0ms

prune217.0ms

localize27.0ms

rewrite21.0ms

series88.0ms

simplify41.0ms

prune177.0ms

localize28.0ms

rewrite31.0ms

series252.0ms

simplify78.0ms

prune271.0ms

localize20.0ms

rewrite49.0ms

series55.0ms

simplify90.0ms

prune208.0ms

regimes483.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze455.0ms

sample884.0ms

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