Details

analyze1.9s

Algorithm: search

sample44.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
4.0ms	42×	body	80	invalid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	18
1	116	18
2	329	18
3	935	18
4	2876	18
5	5001	18

prune5.0ms

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: 29.7b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
0.1b	(* (+ (* z 3.13060547623) 11.1667541262) z)
4.2b	(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
28.0b	(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
5×	`flip3-+` `flip-+`
4×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

10.0ms	(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
7.0ms	(* (+ (* z 3.13060547623) 11.1667541262) z)
14.0ms	(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
25.0ms	(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

series191.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
6.0ms	(* (+ (* z 3.13060547623) 11.1667541262) z)
48.0ms	(* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
133.0ms	(/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

simplify78.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	587	1179
1	2851	995
2	5002	995

prune252.0ms

Filtered

70 candidates to 99 candidates (-41.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	9	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Merged error: 2.8b

Counts

100 → 9

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* 1.6453555072203998 (* y b)))
0.2b	(* 1.6453555072203998 (* y b))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

2 → 29

Calls

2 calls:

2.0ms	(+ x (* 1.6453555072203998 (* y b)))
5.0ms	(* 1.6453555072203998 (* y b))

series11.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(+ x (* 1.6453555072203998 (* y b)))
3.0ms	(* 1.6453555072203998 (* y b))

simplify69.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	149	139
1	529	122
2	2246	122
3	5002	122

prune91.0ms

Filtered

22 candidates to 35 candidates (-59.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	35	9	44

Merged error: 2.8b

Counts

44 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
0.1b	(* (+ (* z 3.13060547623) 11.1667541262) z)
0.1b	(* y (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
27.1b	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
5×	`flip3-+` `flip-+`
4×	`associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 105

Calls

4 calls:

9.0ms	(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
7.0ms	(* (+ (* z 3.13060547623) 11.1667541262) z)
25.0ms	(* y (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
27.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

series194.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ (* (+ z 15.234687407) z) 31.4690115749) z)
6.0ms	(* (+ (* z 3.13060547623) 11.1667541262) z)
132.0ms	(* y (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))
52.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))

simplify83.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	597	1843
1	2682	1632
2	5001	1632

prune274.0ms

Filtered

84 candidates to 117 candidates (-39.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	118	8	126

Merged error: 0.5b

Counts

126 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
8.7b	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
22.5b	(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
23.7b	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

11.0ms	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
11.0ms	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
48.0ms	(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
27.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
6.0ms	(sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))
133.0ms	(* (/ y (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))) (/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))
72.0ms	(/ (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b) (sqrt (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771)))

simplify92.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	673	4330
1	2891	3955
2	5001	3822

prune563.0ms

Filtered

113 candidates to 162 candidates (-43.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	162	8	170

Merged error: 0.5b

Counts

170 → 8

regimes882.0ms

Accuracy

97.8% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 27.6b

bsearch6.2s

Steps

Iters	Range		Point
10	6.56830066736273e+62	2.2773531883785208e+75	6.651986106571032e+62
9	-1.1607121586444226e+32	-2.365531199661495e+26	-6.640265736706856e+31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	26
1	73	26

end0.0ms

analyze2.0s

Algorithm: search

sample1.1s

Algorithm

intervals

Results

699.0ms	8000×	body	80	valid
75.0ms	862×	body	80	invalid

Details

analyze1.9s

sample44.0ms

simplify54.0ms

prune5.0ms

localize24.0ms

rewrite59.0ms

series191.0ms

simplify78.0ms

prune252.0ms

localize5.0ms

rewrite8.0ms

series11.0ms

simplify69.0ms

prune91.0ms

localize23.0ms

rewrite71.0ms

series194.0ms

simplify83.0ms

prune274.0ms

localize28.0ms

rewrite103.0ms

series218.0ms

simplify92.0ms

prune563.0ms

regimes882.0ms

bsearch6.2s

simplify2.0ms

end0.0ms

analyze2.0s

sample1.1s

Profiling