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

sample30.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
2.0ms	27×	body	80	invalid
1.0ms	20×	body	80	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5577	24

prune7.0ms

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: 4.7b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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)
8.0ms	(* (- 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)

series118.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
24.0ms	(* (- x 0.5) (log x))
36.0ms	(- (* (- x 0.5) (log x)) x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify45.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5109	1424

prune225.0ms

Filtered

88 candidates to 108 candidates (-22.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Merged error: 0.0b

Counts

109 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite18.0ms

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)
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series90.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4934	765
1	4934	765

prune147.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 0.0b

Counts

85 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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:

9.0ms	(* (- x 0.5) (log (sqrt x)))
8.0ms	(* (- x 0.5) (log (sqrt x)))
17.0ms	(+ (* (- x 0.5) (log (sqrt x))) (- (* (- x 0.5) (log (sqrt x))) x))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series53.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (- x 0.5) (log (sqrt x)))
8.0ms	(* (- x 0.5) (log (sqrt x)))
13.0ms	(+ (* (- x 0.5) (log (sqrt x))) (- (* (- x 0.5) (log (sqrt x))) x))
25.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4961	2370
1	4961	2370

prune258.0ms

Filtered

110 candidates to 157 candidates (-42.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	158	8	166

Merged error: 0.0b

Counts

166 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
0.3b	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
4.3b	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
66×	`add-sqr-sqrt`
64×	`*-un-lft-identity`
62×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
12×	`log-prod`
11×	`associate-/r/`
8×	`pow1` `div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `div-inv` `associate-/l*` `add-log-exp`
5×	`flip3-+` `associate-l` `flip-+`
4×	`cbrt-undiv` `associate-r`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `flip--`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

7.0ms	(* (- x 0.5) (log x))
7.0ms	(- (* (- x 0.5) (log x)) x)
14.0ms	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
14.0ms	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

series115.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- x 0.5) (log x))
36.0ms	(- (* (- x 0.5) (log x)) x)
25.0ms	(/ 1 (/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333)))
33.0ms	(/ x (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333))

simplify78.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4968	3241
1	4968	3241

prune264.0ms

Filtered

121 candidates to 171 candidates (-41.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	171	8	179

Merged error: 0.0b

Counts

179 → 8

regimes565.0ms

Accuracy

96.4% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 5.9b

bsearch25.0ms

Steps

Iters	Range		Point
7	3215830.134941387	530214421.81041145	3398719.205669345

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	110	83
1	110	83

end0.0ms

sample867.0ms

Algorithm

intervals

Results

525.0ms	8000×	body	80	valid
84.0ms	1238×	body	80	invalid
46.0ms	763×	body	80	nan

Details

analyze459.0ms

sample30.0ms

simplify105.0ms

prune7.0ms

localize16.0ms

rewrite42.0ms

series118.0ms

simplify45.0ms

prune225.0ms

localize25.0ms

rewrite18.0ms

series90.0ms

simplify55.0ms

prune147.0ms

localize20.0ms

rewrite50.0ms

series53.0ms

simplify55.0ms

prune258.0ms

localize18.0ms

rewrite48.0ms

series115.0ms

simplify78.0ms

prune264.0ms

regimes565.0ms

bsearch25.0ms

simplify2.0ms

end0.0ms

sample867.0ms

Profiling