Details

analyze2.7s

Algorithm

sampling

Space saved by range analysis: 0.243902%

Space saved by search: 1.437274%

Guaranteed chance to sample good point: 35.739437%

sample28.0ms

Algorithm

intervals

Results

8.0ms	215×	body	80	valid
2.0ms	15×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	28×	body	80	invalid
1.0ms	5×	body	1280	valid
1.0ms	7×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	6

prune4.0ms

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: 24.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
1.7b	(+ x (/ (* (- y x) (- z t)) (- a t)))
18.5b	(/ (* (- y x) (- z t)) (- a t))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
7.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
16.0ms	(/ (* (- y x) (- z t)) (- a t))

series93.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
52.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
32.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune144.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 2.3b

Counts

91 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.7b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.7b	(* (- y x) (/ (- z t) (- a t)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

8.0ms	(/ (- z t) (- a t))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
17.0ms	(* (- y x) (/ (- z t) (- a t)))

series94.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- z t) (- a t))
50.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
34.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify52.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	476	869
1	2018	820
2	5002	820

prune153.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	125	13	138

Merged error: 2.3b

Counts

138 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ z (- a t))
0.0b	(/ t (- a t))
1.7b	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))
2.7b	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
48×	`times-frac`
28×	`add-cube-cbrt`
21×	`distribute-lft-out--`
18×	`associate-r`
15×	`difference-of-squares`
12×	`flip3--` `flip--`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
8×	`frac-times` `associate-/r/`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`associate-l`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `associate-*r/` `div-inv`
3×	`distribute-rgt-out--` `frac-sub` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

5.0ms	(/ z (- a t))
5.0ms	(/ t (- a t))
7.0ms	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))
38.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ z (- a t))
5.0ms	(/ t (- a t))
55.0ms	(+ x (* (- y x) (- (/ z (- a t)) (/ t (- a t)))))
35.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))

simplify76.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	581	1057
1	2586	1012
2	5002	1012

prune193.0ms

Filtered

113 candidates to 154 candidates (-36.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	156	11	167

Merged error: 1.4b

Counts

167 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.7b	(+ x (/ (- y x) (/ (- a t) (- z t))))
3.0b	(/ (- y x) (/ (- a t) (- z t)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

8.0ms	(/ (- a t) (- z t))
41.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
20.0ms	(/ (- y x) (/ (- a t) (- z t)))

series104.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- a t) (- z t))
52.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
43.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify104.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1030	3053
1	4263	2984
2	5001	2984

prune214.0ms

Filtered

170 candidates to 283 candidates (-66.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	281	2	283
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	284	10	294

Merged error: 1.4b

Counts

294 → 10

Details

analyze2.7s

sample28.0ms

simplify61.0ms

prune4.0ms

localize9.0ms

rewrite34.0ms

series93.0ms

simplify52.0ms

prune144.0ms

localize9.0ms

rewrite33.0ms

series94.0ms

simplify52.0ms

prune153.0ms

localize11.0ms

rewrite60.0ms

series103.0ms

simplify76.0ms

prune193.0ms

localize10.0ms

rewrite89.0ms

series104.0ms

simplify104.0ms

prune214.0ms

regimes484.0ms

bsearch1.0ms

Profiling