Details

sample94.0ms

Algorithm

intervals

Results

32.0ms	382×	body	80	valid
27.0ms	390×	body	80	nan

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (16.0ms)

Iter	Nodes	Cost
0	40	12
1	92	12
2	269	12
3	669	12
4	1565	11
5	2855	11
6	5001	11

prune12.0ms

Filtered

1 candidates to 1 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: 5.7b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`frac-sub`
7×	`flip3--` `flip--`
6×	`associate-/l/`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`sub-neg` `associate-*l/` `div-inv` `associate--r+`
1×	`fma-neg` `*-commutative` `fma-udef` `associate--r-`

Counts

4 → 27

Calls

4 calls:

11.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
6.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
9.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series310.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
114.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	549	531
1	2536	498
2	5001	489

prune169.0ms

Filtered

39 candidates to 32 candidates (82.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	31	8	39
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	33	8	41

Merged error: 3.2b

Counts

41 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.2b	(* (log x) (- x 0.5))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

26×	`flip3--` `associate-*r/` `flip--`
24×	`frac-add`
20×	`frac-sub`
10×	`associate-/l/`
6×	`sub-neg` `flip3-+` `flip-+`
5×	`frac-2neg` `clear-num`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
3×	`associate-+r-` `associate-+r+` `*-commutative`
2×	`fma-def` `associate-*l/` `associate--r+`
1×	`+-commutative` `div-inv` `associate--r-`

Counts

4 → 54

Calls

4 calls:

6.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
17.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
3.0ms	(* (log x) (- x 0.5))
9.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series514.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
130.0ms	(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
242.0ms	(* (log x) (- x 0.5))
78.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1042	1647
1	5001	1566

prune348.0ms

Filtered

66 candidates to 55 candidates (83.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	62	12	74

Merged error: 3.2b

Counts

74 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.0007936500793651 (pow z 2))
0.2b	(* (log x) (- x 0.5))
5.3b	(/ (+ (fma y (pow z 2) (- (* 0.0007936500793651 (pow z 2)) (* 0.0027777777777778 z))) 0.083333333333333) x)
5.6b	(fma y (pow z 2) (- (* 0.0007936500793651 (pow z 2)) (* 0.0027777777777778 z)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r/` `associate-r` `-commutative` `associate-/l/`
1×	`flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 16

Calls

4 calls:

3.0ms	(* 0.0007936500793651 (pow z 2))
3.0ms	(* (log x) (- x 0.5))
3.0ms	(/ (+ (fma y (pow z 2) (- (* 0.0007936500793651 (pow z 2)) (* 0.0027777777777778 z))) 0.083333333333333) x)
1.0ms	(fma y (pow z 2) (- (* 0.0007936500793651 (pow z 2)) (* 0.0027777777777778 z)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.0007936500793651 (pow z 2))
255.0ms	(* (log x) (- x 0.5))
80.0ms	(/ (+ (fma y (pow z 2) (- (* 0.0007936500793651 (pow z 2)) (* 0.0027777777777778 z))) 0.083333333333333) x)
47.0ms	(fma y (pow z 2) (- (* 0.0007936500793651 (pow z 2)) (* 0.0027777777777778 z)))

simplify62.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	187	157
1	515	151
2	2149	144
3	5001	138

prune117.0ms

Filtered

28 candidates to 16 candidates (57.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	25	3	28
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	29	11	40

Merged error: 3.2b

Counts

40 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (log x) (- x 0.5) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
0.2b	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
5.3b	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-/r/`
4×	`clear-num`
3×	`frac-2neg` `associate-/r*` `div-inv`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`flip3--` `*-commutative` `flip--` `fma-udef` `remove-double-div` `inv-pow`

Counts

4 → 20

Calls

4 calls:

6.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
9.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
8.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

series352.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
115.0ms	(fma (log x) (- x 0.5) (- (/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))) (- x 0.91893853320467)))
86.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
109.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

simplify101.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	276	220
1	919	204
2	4249	188
3	5001	179

prune112.0ms

Filtered

32 candidates to 27 candidates (84.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	31	12	43

Merged error: 2.2b

Counts

43 → 12

regimes484.0ms

Accuracy

84.1% (0.6b remaining)

Error of 2.4b against oracle of 1.8b and baseline of 5.8b

bsearch168.0ms

Steps

Iters	Range		Point
7	8.989489765620377e+131	4.887283975934777e+133	6.521488710118406e+132
9	2697524.489058797	555429331548894.9	41606032291.84351

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	42
1	74	42
2	74	42

end0.0ms

sample1.8s

Algorithm

intervals

Results

658.0ms	11646×	body	80	valid
567.0ms	11744×	body	80	nan