Details

analyze1.6s

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 18.436034%

Guaranteed chance to sample good point: 51.919411%

sample46.0ms

Algorithm

intervals

Results

9.0ms	185×	body	80	valid
6.0ms	31×	body	1280	nan
5.0ms	22×	body	1280	valid
5.0ms	26×	body	640	valid
3.0ms	22×	body	640	nan
2.0ms	16×	body	320	valid
2.0ms	17×	body	320	nan
1.0ms	7×	body	160	valid
0.0ms	7×	body	160	nan
0.0ms	12×	body	80	nan

simplify17.0ms

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

prune3.0ms

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: 17.4b

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))
1.8b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.2b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite55.0ms

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)))
14.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
6.0ms	(/ (- x y) (- 1.0 y))
9.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
15.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify44.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	495	950
1	1433	898
2	5002	876

prune198.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	4	121

Merged error: 0b

Counts

121 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- 1.0 y))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
3.2b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
4.2b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-cube-cbrt`
21×	`associate-r`
18×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`flip3--` `flip--` `add-log-exp`
5×	`associate-l` `associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`log-prod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `log-div` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `log-pow` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 117

Calls

4 calls:

5.0ms	(/ 1 (- 1.0 y))
14.0ms	(* (- x y) (/ 1 (- 1.0 y)))
2.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
3.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1 (- 1.0 y))
6.0ms	(* (- x y) (/ 1 (- 1.0 y)))
12.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
12.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify51.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	487	838
1	1987	738
2	5002	686

prune148.0ms

Filtered

82 candidates to 129 candidates (-57.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	129	4	133

Merged error: 0b

Counts

133 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
1.8b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
69×	`times-frac`
37×	`add-cube-cbrt`
28×	`difference-of-squares`
24×	`log-prod`
20×	`distribute-lft-out--`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
3×	`div-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 144

Calls

4 calls:

16.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
17.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
6.0ms	(/ (- x y) (- 1.0 y))
16.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
12.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify55.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	621	1546
1	1974	1467
2	5001	1448

prune259.0ms

Filtered

118 candidates to 156 candidates (-32.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	156	4	160

Merged error: 0b

Counts

160 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

1.8b	(- 1.0 (/ (- x y) (- 1.0 y)))
1.8b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.0b	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
3.0b	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
18×	`log-prod`
16×	`*-un-lft-identity`
12×	`cbrt-prod`
8×	`add-cube-cbrt` `add-log-exp` `difference-of-squares`
6×	`pow1` `add-exp-log`
4×	`log-div` `cbrt-div` `flip3--` `times-frac` `log-pow` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`sub-neg` `pow1/3` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 74

Calls

4 calls:

14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
15.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
14.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
9.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
20.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
20.0ms	(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	247	858
1	562	794
2	2172	778
3	5001	762

prune186.0ms

Filtered

68 candidates to 86 candidates (-26.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	86	4	90

Merged error: 0b

Counts

90 → 4

Details

analyze1.6s

sample46.0ms

simplify17.0ms

prune3.0ms

localize8.0ms

rewrite55.0ms

series45.0ms

simplify44.0ms

prune198.0ms

localize9.0ms

rewrite28.0ms

series33.0ms

simplify51.0ms

prune148.0ms

localize10.0ms

rewrite59.0ms

series54.0ms

simplify55.0ms

prune259.0ms

localize12.0ms

rewrite62.0ms

series61.0ms

simplify61.0ms

prune186.0ms

regimes252.0ms

bsearch1.0ms

Profiling