Details

sample43.0ms

Algorithm

intervals

Results

24.0ms

765×

body

valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	4
1	41	4
2	102	4
3	228	4
4	411	4
5	786	4
6	2469	4
7	5002	4

prune2.0ms

Filtered

1 candidates to 0 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: 7.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
6.6b	(/ (* (cosh x) (/ y x)) z)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `cosh-def` `prod-exp` `cbrt-unprod`
3×	`associate-l` `associate-/r*` `associate-/l/`
2×	`expm1-log1p-u` `frac-times` `associate-r/` `associate-l/` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

2 → 64

Calls

2 calls:

7.0ms	(* (cosh x) (/ y x))
6.0ms	(/ (* (cosh x) (/ y x)) z)

series186.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(* (cosh x) (/ y x))
110.0ms	(/ (* (cosh x) (/ y x)) z)

simplify44.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	352	391
1	1472	333
2	5001	333

prune138.0ms

Filtered

70 candidates to 53 candidates (75.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	9	71

Merged error: 0.0b

Counts

71 → 9

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (exp (* -1 x)) (* 1/2 (exp x)))
0.2b	(/ (fma 1/2 (exp (* -1 x)) (* 1/2 (exp x))) (/ x y))
6.6b	(/ (/ (fma 1/2 (exp (* -1 x)) (* 1/2 (exp x))) (/ x y)) z)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

471×	`times-frac`
230×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
47×	`associate-/l*`
22×	`div-inv`
17×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
9×	`cbrt-undiv` `div-exp`
5×	`associate-/r/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 280

Calls

3 calls:

1.0ms	(fma 1/2 (exp (* -1 x)) (* 1/2 (exp x)))
6.0ms	(/ (fma 1/2 (exp (* -1 x)) (* 1/2 (exp x))) (/ x y))
13.0ms	(/ (/ (fma 1/2 (exp (* -1 x)) (* 1/2 (exp x))) (/ x y)) z)

series239.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(fma 1/2 (exp (* -1 x)) (* 1/2 (exp x)))
77.0ms	(/ (fma 1/2 (exp (* -1 x)) (* 1/2 (exp x))) (/ x y))
111.0ms	(/ (/ (fma 1/2 (exp (* -1 x)) (* 1/2 (exp x))) (/ x y)) z)

simplify78.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1181	4690
1	5001	4522

prune1.1s

Filtered

289 candidates to 252 candidates (87.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	286	3	289
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	289	9	298

Merged error: 0b

Counts

298 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (cosh x) y)
0.3b	(* (* (cosh x) y) (/ 1 x))
6.6b	(/ (* (* (cosh x) y) (/ 1 x)) z)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
35×	`add-cbrt-cube`
25×	`prod-exp`
17×	`div-exp`
16×	`add-sqr-sqrt` `associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-unprod`
12×	`times-frac`
10×	`pow1`
9×	`cbrt-undiv`
7×	`associate-*l/`
5×	`cosh-def`
4×	`rec-exp` `1-exp` `associate-l` `pow-prod-down` `associate-/l/`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `associate-r/` `un-div-inv` `-commutative` `div-inv`
1×	`frac-2neg` `clear-num` `associate-/l*` `unswap-sqr`

Counts

3 → 100

Calls

3 calls:

4.0ms	(* (cosh x) y)
8.0ms	(* (* (cosh x) y) (/ 1 x))
10.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)

series262.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* (cosh x) y)
74.0ms	(* (* (cosh x) y) (/ 1 x))
119.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)

simplify77.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	532	637
1	2730	501
2	5002	485

prune165.0ms

Filtered

109 candidates to 67 candidates (61.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	111	7	118

Merged error: 0b

Counts

118 → 7

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y (* x z)))
6.8b	(/ y (* x z))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`times-frac`
5×	`prod-exp` `cbrt-unprod`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`associate-l` `associate-/l*`
2×	`expm1-log1p-u` `cosh-def` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `unswap-sqr`

Counts

2 → 54

Calls

2 calls:

7.0ms	(* (cosh x) (/ y (* x z)))
5.0ms	(/ y (* x z))

series141.0ms

Counts

2 → 6

Calls

2 calls:

121.0ms	(* (cosh x) (/ y (* x z)))
20.0ms	(/ y (* x z))

simplify41.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	266	305
1	1075	254
2	5001	252

prune93.0ms

Filtered

60 candidates to 42 candidates (70.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	61	6	67

Merged error: 0b

Counts

67 → 6

regimes150.0ms

Accuracy

95% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 7.5b

bsearch103.0ms

Steps

Iters	Range		Point
10	5.91444132257046e+46	4.9701672827403295e+57	8.261310087671331e+52
8	-4.36457954397458e+31	-5.589317017320754e+28	-3.345163590317331e+30

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	11
1	26	11

end0.0ms

sample1.2s

Algorithm

intervals

Results

732.0ms

22825×

body

valid