Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	190×	body	80	valid
6.0ms	29×	body	1280	valid
5.0ms	20×	body	640	valid
3.0ms	120×	body	80	nan
3.0ms	19×	body	1280	nan
1.0ms	11×	body	640	nan
1.0ms	12×	body	320	valid
0.0ms	4×	body	320	nan
0.0ms	5×	body	160	valid
0.0ms	4×	body	160	nan

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

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: 16.2b

Counts

2 → 1

localize8.0ms

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))
1.3b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.7b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite57.0ms

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`
9×	`add-log-exp`
7×	`add-exp-log`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`diff-log` `associate--r-`
2×	`sub-neg` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 109

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))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
42.0ms	(/ (- x y) (- 1.0 y))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
88.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	483	948
1	1374	900
2	5002	882

prune226.0ms

Filtered

121 candidates to 88 candidates (72.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	4	122

Merged error: 0.1b

Counts

122 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(cbrt (- 1.0 y))
5.7b	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
10.7b	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

535×	`add-sqr-sqrt`
184×	`times-frac`
162×	`unswap-sqr`
120×	`cbrt-prod`
118×	`difference-of-squares`
75×	`*-un-lft-identity`
64×	`log-prod`
24×	`swap-sqr`
12×	`*-commutative`
8×	`distribute-lft-out--`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `flip3--` `associate-l` `add-cbrt-cube` `flip--`
2×	`log-div` `pow1/3` `div-inv`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 178

Calls

4 calls:

3.0ms	(cbrt (- 1.0 y))
3.0ms	(cbrt (- 1.0 y))
143.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
138.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (- 1.0 y))
95.0ms	(cbrt (- 1.0 y))
98.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
66.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	807	4488
1	1983	4402
2	5001	4300

prune374.0ms

Filtered

190 candidates to 108 candidates (56.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	190	4	194

Merged error: 0.1b

Counts

194 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- x y) (- 1.0 y)) 3)
1.2b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
5.7b	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
12.3b	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

588×	`*-un-lft-identity`
437×	`add-sqr-sqrt`
370×	`times-frac`
235×	`unpow-prod-down`
214×	`difference-of-squares`
176×	`associate-l` `distribute-lft-out`
153×	`log-prod`
120×	`sqr-pow`
77×	`add-cube-cbrt`
71×	`pow-unpow`
68×	`difference-cubes`
45×	`distribute-lft-out--`
44×	`associate-/l*`
33×	`log-div`
14×	`associate-/r*`
12×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1` `associate-/r/` `add-log-exp`
4×	`flip3--` `flip--` `associate-/l/`
3×	`div-exp` `log-rec` `clear-num` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `rem-log-exp` `pow-exp` `flip-+` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `unpow3` `div-sub` `log-pow`

Counts

4 → 470

Calls

4 calls:

9.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
26.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
108.0ms	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
97.0ms	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

series948.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
197.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
386.0ms	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
293.0ms	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

simplify230.0ms

Algorithm

egg-herbie

Counts

482 → 482

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1442	12387
1	4935	12114
2	5002	12114

prune905.0ms

Filtered

482 candidates to 229 candidates (47.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	480	2	482
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	481	5	486

Merged error: 0.1b

Counts

486 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
1.2b	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
3.8b	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
5.8b	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

638×	`add-sqr-sqrt`
459×	`*-un-lft-identity`
225×	`frac-times`
212×	`times-frac`
202×	`difference-of-squares`
162×	`associate-/l*`
160×	`associate-/r*`
151×	`distribute-lft-out--`
122×	`add-cube-cbrt`
97×	`swap-sqr`
64×	`associate-/l/`
62×	`unswap-sqr`
57×	`log-prod`
39×	`associate-l`
38×	`flip3--` `flip--`
33×	`clear-num`
32×	`frac-2neg`
31×	`associate-r`
29×	`*-commutative`
18×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`associate-r/` `associate-l/`
13×	`pow1`
8×	`associate-/r/`
6×	`add-log-exp`
4×	`cbrt-undiv` `log-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
3×	`un-div-inv`
2×	`rem-log-exp` `log-pow`
1×	`pow2` `sub-neg` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+` `distribute-lft-out`

Counts

4 → 541

Calls

4 calls:

46.0ms	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
116.0ms	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
114.0ms	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
12.0ms	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
111.0ms	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
353.0ms	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
93.0ms	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

simplify122.0ms

Algorithm

egg-herbie

Counts

553 → 553

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1779	6903
1	5002	6334

prune874.0ms

Filtered

553 candidates to 197 candidates (35.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	552	1	553
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	554	4	558

Merged error: 0.1b

Counts

558 → 4

regimes87.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 16.5b

bsearch139.0ms

Steps

Iters	Range		Point
10	2.622148067335985e-09	55266295.648746796	27970212.32870033
9	-21360866922585.72	-5585.32673263024	-42675037.631414294

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	23
1	38	23

end0.0ms

sample1.0s

Algorithm

intervals

Results

224.0ms	5737×	body	80	valid
155.0ms	785×	body	1280	valid
106.0ms	778×	body	640	valid
102.0ms	3602×	body	80	nan
58.0ms	361×	body	1280	nan
49.0ms	463×	body	320	valid
47.0ms	380×	body	640	nan
19.0ms	220×	body	320	nan
18.0ms	237×	body	160	valid
6.0ms	105×	body	160	nan