Details

analyze468.0ms

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

sample33.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
2.0ms	34×	body	80	invalid
1.0ms	21×	body	80	nan

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5577	24

prune12.0ms

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: 3.0b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
0.1b	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
0.2b	(* (- x 0.5) (log x))
2.7b	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

9.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
21.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
7.0ms	(* (- x 0.5) (log x))
12.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

series77.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778))
30.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x) x)))
24.0ms	(* (- x 0.5) (log x))
15.0ms	(/ (+ (* z (- (* (+ y 0.0007936500793651) z) 0.0027777777777778)) 0.083333333333333) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5114	2223

prune258.0ms

Filtered

93 candidates to 117 candidates (-25.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Merged error: 0.0b

Counts

119 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log (sqrt x)))
0.2b	(* (- x 0.5) (log (sqrt x)))
0.3b	(+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))
2.7b	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `log-prod`
32×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
12×	`pow1` `associate-+r+` `associate-r`
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-+l-` `sub-neg` `associate-+l+` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 133

Calls

4 calls:

8.0ms	(* (- x 0.5) (log (sqrt x)))
8.0ms	(* (- x 0.5) (log (sqrt x)))
9.0ms	(+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))
11.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (- x 0.5) (log (sqrt x)))
7.0ms	(* (- x 0.5) (log (sqrt x)))
15.0ms	(+ (- 0.91893853320467 x) (* (- x 0.5) (log (sqrt x))))
16.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

simplify36.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5011	2191

prune244.0ms

Filtered

101 candidates to 145 candidates (-43.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	145	11	156

Merged error: 0.0b

Counts

156 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.7b	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

rewrite16.0ms

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

series84.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
21.0ms	(cbrt x)
24.0ms	(cbrt x)
16.0ms	(/ (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333) x)

simplify42.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5046	765

prune148.0ms

Filtered

56 candidates to 74 candidates (-32.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	74	11	85

Merged error: 0.0b

Counts

85 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ 1 (/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333))) x)))
0.2b	(* (- x 0.5) (log x))
0.3b	(/ 1 (/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333)))
2.6b	(/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333))

rewrite71.0ms

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` `add-log-exp`
12×	`log-prod`
11×	`associate-/r/`
8×	`pow1` `flip3-+` `div-exp` `flip-+`
6×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-l/` `div-inv` `associate-/l`
5×	`associate-l` `sum-log`
4×	`cbrt-undiv` `associate-r` `frac-add`
3×	`flip3--` `flip--`
2×	`associate-+r-` `rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`+-commutative` `associate-+r+` `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 → 167

Calls

4 calls:

34.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ 1 (/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333))) x)))
7.0ms	(* (- x 0.5) (log x))
14.0ms	(/ 1 (/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333)))
11.0ms	(/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333))

series112.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* (- x 0.5) (log x)) (+ 0.91893853320467 (- (/ 1 (/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333))) x)))
21.0ms	(* (- x 0.5) (log x))
23.0ms	(/ 1 (/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333)))
36.0ms	(/ x (+ (* z (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)) 0.083333333333333))

simplify82.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4969	4067
1	4969	4067

prune271.0ms

Filtered

123 candidates to 179 candidates (-45.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	179	11	190

Merged error: 0.0b

Counts

190 → 11

regimes350.0ms

Accuracy

95.9% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 6.0b

bsearch35.0ms

Steps

Iters	Range		Point
9	1806.8211942563867	127931370.3875123	477006.7565026866

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	106	75
1	106	75

end0.0ms

sample924.0ms

Algorithm

intervals

Results

564.0ms	8000×	body	80	valid
89.0ms	1287×	body	80	invalid
45.0ms	694×	body	80	nan

Details

analyze468.0ms

sample33.0ms

simplify107.0ms

prune12.0ms

localize20.0ms

rewrite51.0ms

series77.0ms

simplify65.0ms

prune258.0ms

localize19.0ms

rewrite40.0ms

series45.0ms

simplify36.0ms

prune244.0ms

localize24.0ms

rewrite16.0ms

series84.0ms

simplify42.0ms

prune148.0ms

localize19.0ms

rewrite71.0ms

series112.0ms

simplify82.0ms

prune271.0ms

regimes350.0ms

bsearch35.0ms

simplify2.0ms

end0.0ms

sample924.0ms

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