Details

sample41.0ms

Algorithm

intervals

Results

22.0ms

776×

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: 7.7b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) (/ y x))
7.3b	(/ (* (cosh x) (/ y x)) z)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

1.0ms	(cosh x)
7.0ms	(* (cosh x) (/ y x))
9.0ms	(/ (* (cosh x) (/ y x)) z)

series240.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(cosh x)
79.0ms	(* (cosh x) (/ y x))
117.0ms	(/ (* (cosh x) (/ y x)) z)

simplify49.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	383	433
1	1634	372
2	5001	368

prune192.0ms

Filtered

83 candidates to 65 candidates (78.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	7	84

Merged error: 0.0b

Counts

84 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) y)
5.8b	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log` `add-cbrt-cube`
10×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`cbrt-undiv` `add-cube-cbrt` `div-exp`
5×	`pow1` `add-log-exp`
4×	`associate-l` `associate-*l/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `associate-r` `flip-+` `log1p-expm1-u`
2×	`associate-/l/` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

5.0ms	(+ (exp x) (exp (- x)))
7.0ms	(* (+ (exp x) (exp (- x))) y)
11.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

series175.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (exp x) (exp (- x)))
53.0ms	(* (+ (exp x) (exp (- x))) y)
99.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	435	681
1	2498	531
2	5001	530

prune205.0ms

Filtered

78 candidates to 56 candidates (71.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Merged error: 0.0b

Counts

85 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) (exp (- x))) y) z)
0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) y)
6.3b	(/ (/ (* (+ (exp x) (exp (- x))) y) z) (* 2 x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
17×	`*-un-lft-identity`
16×	`times-frac`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `associate-l/` `associate-/r` `log1p-expm1-u` `div-inv`
3×	`fma-def` `flip3-+` `associate-r` `flip-+` `associate-/l/`
2×	`frac-2neg` `clear-num` `distribute-lft-out`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

8.0ms	(/ (* (+ (exp x) (exp (- x))) y) z)
5.0ms	(+ (exp x) (exp (- x)))
11.0ms	(* (+ (exp x) (exp (- x))) y)
11.0ms	(/ (/ (* (+ (exp x) (exp (- x))) y) z) (* 2 x))

series241.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (* (+ (exp x) (exp (- x))) y) z)
28.0ms	(+ (exp x) (exp (- x)))
52.0ms	(* (+ (exp x) (exp (- x))) y)
96.0ms	(/ (/ (* (+ (exp x) (exp (- x))) y) z) (* 2 x))

simplify82.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	507	1005
1	2589	818
2	5001	811

prune293.0ms

Filtered

117 candidates to 85 candidates (72.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	118	7	125

Merged error: 0.0b

Counts

125 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (exp x) 1/2 (/ 1/2 (exp x)))
0.0b	(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
0.0b	(/ 1/2 (exp x))
6.4b	(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
19×	`add-exp-log`
13×	`associate-r` `associate-l`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 120

Calls

4 calls:

1.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
3.0ms	(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
4.0ms	(/ 1/2 (exp x))
9.0ms	(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

series259.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
70.0ms	(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
9.0ms	(/ 1/2 (exp x))
144.0ms	(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

simplify70.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	509	1056
1	2478	943
2	5002	942

prune340.0ms

Filtered

132 candidates to 102 candidates (77.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	132	7	139

Merged error: 0.0b

Counts

139 → 7

regimes211.0ms

Accuracy

96.6% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 6.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

611.0ms

22188×

body

valid