Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	178×	body	80	valid
5.0ms	25×	body	1280	valid
3.0ms	109×	body	80	nan
3.0ms	22×	body	640	valid
2.0ms	13×	body	1280	nan
2.0ms	19×	body	320	valid
2.0ms	15×	body	640	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	4×	body	160	nan

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
13.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms	(/ (- x y) (- 1.0 y))
50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
98.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify46.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	488	942
1	1388	894
2	5001	876

prune283.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- x y))
0.6b	(cbrt (- x y))
3.8b	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
11.9b	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`log-prod`
2×	`log-div` `pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 56

Calls

4 calls:

6.0ms	(cbrt (- x y))
5.0ms	(cbrt (- x y))
4.0ms	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
5.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

series578.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (- x y))
185.0ms	(cbrt (- x y))
113.0ms	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
74.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

simplify128.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	304	790
1	850	697
2	3564	675
3	5001	665

prune204.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

3.5b	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
3.5b	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
11.9b	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))
11.9b	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`add-exp-log` `sqrt-prod` `log-pow`
4×	`log-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp`

Counts

4 → 62

Calls

4 calls:

3.0ms	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
3.0ms	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
3.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))
3.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
126.0ms	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
54.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))
54.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

simplify85.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	215	1418
1	611	1274
2	2895	1270
3	5001	1266

prune248.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x (pow y 2)) (/ 1 y))
2.2b	(log (+ (* 1.0 (- (/ x (pow y 2)) (/ 1 y))) (/ x y)))
4.3b	(+ (* 1.0 (- (/ x (pow y 2)) (/ 1 y))) (/ x y))
10.0b	(/ x (pow y 2))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
48×	`times-frac`
34×	`*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`unpow-prod-down` `difference-of-squares`
10×	`add-exp-log`
8×	`associate-/r*` `add-log-exp`
7×	`unpow2` `sqr-pow`
6×	`associate-*r/` `frac-add` `add-cbrt-cube`
5×	`pow1` `log-div`
4×	`associate-+l+`
3×	`sub-neg` `log-prod` `flip3--` `div-exp` `frac-sub` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 115

Calls

4 calls:

26.0ms	(- (/ x (pow y 2)) (/ 1 y))
26.0ms	(log (+ (* 1.0 (- (/ x (pow y 2)) (/ 1 y))) (/ x y)))
29.0ms	(+ (* 1.0 (- (/ x (pow y 2)) (/ 1 y))) (/ x y))
5.0ms	(/ x (pow y 2))

series150.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ x (pow y 2)) (/ 1 y))
65.0ms	(log (+ (* 1.0 (- (/ x (pow y 2)) (/ 1 y))) (/ x y)))
32.0ms	(+ (* 1.0 (- (/ x (pow y 2)) (/ 1 y))) (/ x y))
23.0ms	(/ x (pow y 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	519	1121
1	1896	1014
2	5002	1005

prune277.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes105.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.5b

bsearch142.0ms

Steps

Iters	Range		Point
11	0.04032056371688071	1.4819289714344828e+28	73789365.95162582
8	-1398402063.149054	-3875183.9477288676	-73256728.01718603

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	50
1	43	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

223.0ms	5679×	body	80	valid
172.0ms	837×	body	1280	valid
110.0ms	772×	body	640	valid
105.0ms	3645×	body	80	nan
57.0ms	365×	body	1280	nan
52.0ms	463×	body	320	valid
47.0ms	405×	body	640	nan
20.0ms	239×	body	320	nan
17.0ms	249×	body	160	valid
6.0ms	109×	body	160	nan