Details

sample87.0ms

Algorithm

intervals

Results

29.0ms	373×	body	80	valid
26.0ms	400×	body	80	nan

simplify53.0ms

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

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: 4.5b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite39.0ms

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:

7.0ms	(* (- x 0.5) (log x))
6.0ms	(- (* (- x 0.5) (log x)) x)
12.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series116.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- x 0.5) (log x))
37.0ms	(- (* (- x 0.5) (log x)) x)
36.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	543	875
1	1813	820
2	5001	763

prune235.0ms

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: 4.0b

Counts

111 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite15.0ms

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:

24.0ms	(cbrt x)
21.0ms	(cbrt x)
21.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify97.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (90.0ms)

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

prune168.0ms

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: 4.0b

Counts

86 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x)
0.2b	(+ (- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x) 0.91893853320467)
0.5b	(* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x))))
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

53×	`pow1`
28×	`sqrt-pow1`
20×	`pow-prod-down`
19×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`associate-*l/`
12×	`sqrt-div`
11×	`add-log-exp`
10×	`pow1/2` `pow-prod-up`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3--` `flip--`
6×	`pow-sqr`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `sqrt-prod`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `associate-+l+` `flip3-+` `diff-log` `associate-*r/` `sum-log` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `associate-+l-` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

16.0ms	(- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x)
17.0ms	(+ (- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x) 0.91893853320467)
16.0ms	(* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x))))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series131.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x)
35.0ms	(+ (- (* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x)))) x) 0.91893853320467)
39.0ms	(* (sqrt (* (- x 0.5) (log x))) (sqrt (* (- x 0.5) (log x))))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify105.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	898	1515
1	4150	1335
2	5002	1311

prune309.0ms

Filtered

127 candidates to 83 candidates (34.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	127	12	139

Merged error: 4.0b

Counts

139 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
4.3b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

7.0ms	(* (- x 0.5) (log x))
6.0ms	(- (* (- x 0.5) (log x)) x)
10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
15.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series114.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- x 0.5) (log x))
34.0ms	(- (* (- x 0.5) (log x)) x)
38.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
21.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify65.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	654	975
1	2582	892
2	5003	833

prune168.0ms

Filtered

121 candidates to 88 candidates (27.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	121	12	133

Merged error: 4.0b

Counts

133 → 12

regimes540.0ms

Accuracy

0% (1.3b remaining)

Error of 6.0b against oracle of 4.6b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample2.5s

Algorithm

intervals

Results

842.0ms	11665×	body	80	valid
777.0ms	11882×	body	80	nan

Details

sample87.0ms

simplify53.0ms

prune4.0ms

localize16.0ms

rewrite39.0ms

series116.0ms

simplify52.0ms

prune235.0ms

localize25.0ms

rewrite15.0ms

series88.0ms

simplify97.0ms

prune168.0ms

localize19.0ms

rewrite63.0ms

series131.0ms

simplify105.0ms

prune309.0ms

localize17.0ms

rewrite42.0ms

series114.0ms

simplify65.0ms

prune168.0ms

regimes540.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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