Details

sample39.0ms

Algorithm

intervals

Results

9.0ms	260×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	11×	body	160	valid

simplify60.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 26.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.3b	(+ x (/ (* (- y x) (- z t)) (- a t)))
18.7b	(/ (* (- y x) (- z t)) (- a t))

rewrite29.0ms

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:

8.0ms	(* (- y x) (- z t))
7.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
11.0ms	(/ (* (- y x) (- z t)) (- a t))

series314.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* (- y x) (- z t))
154.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
120.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune458.0ms

Filtered

90 candidates to 67 candidates (25.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	76	14	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	14	91

Merged error: 6.0b

Counts

91 → 14

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.7b	(/ (- y x) (/ (- a t) (- z t)))
3.3b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite79.0ms

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:

7.0ms	(/ (- a t) (- z t))
14.0ms	(/ (- y x) (/ (- a t) (- z t)))
38.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series451.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (- a t) (- z t))
235.0ms	(/ (- y x) (/ (- a t) (- z t)))
160.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify112.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (25.0ms)

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

prune2.2s

Filtered

283 candidates to 172 candidates (39.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	276	7	283
Fresh	10	3	13
Picked	0	1	1
Done	0	0	0
Total	286	11	297

Merged error: 6.0b

Counts

297 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- z t))
0.6b	(cbrt (- z t))
1.7b	(/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t))))
7.7b	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

1766×	`times-frac`
1047×	`*-un-lft-identity`
1045×	`add-sqr-sqrt`
592×	`cbrt-div`
520×	`cbrt-prod`
455×	`add-cube-cbrt`
397×	`associate-/r/`
297×	`flip3--` `flip--`
295×	`distribute-lft-out--` `difference-of-squares`
192×	`frac-times`
142×	`associate-/r*`
96×	`associate-r/` `associate-l/`
55×	`div-inv`
18×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`associate-/l*`
4×	`pow1`
2×	`pow1/3` `div-sub` `associate-/l/`
1×	`+-commutative` `associate-+r-` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 922

Calls

4 calls:

3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
48.0ms	(/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t))))
148.0ms	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (- z t))
165.0ms	(cbrt (- z t))
219.0ms	(/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t))))
182.0ms	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))

simplify243.0ms

Algorithm

egg-herbie

Counts

934 → 934

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	3861	22151
1	5003	22089

prune26.1s

Filtered

934 candidates to 554 candidates (40.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	932	2	934
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	933	12	945

Merged error: 6.0b

Counts

945 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

1.7b	(/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t))))
7.7b	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))
7.7b	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))
7.7b	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))

rewrite603.0ms

Algorithm

rewrite-expression-head

Rules

1766×	`times-frac`
1045×	`*-un-lft-identity`
1039×	`add-sqr-sqrt`
588×	`cbrt-div`
510×	`cbrt-prod`
453×	`add-cube-cbrt`
397×	`associate-/r/`
295×	`flip3--` `flip--`
293×	`distribute-lft-out--` `difference-of-squares`
192×	`frac-times`
142×	`associate-/r*`
96×	`associate-r/` `associate-l/`
55×	`div-inv`
18×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`add-log-exp`
9×	`cbrt-undiv` `div-exp`
5×	`associate-/l*`
4×	`pow1` `div-sub`
3×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
2×	`associate-/l/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`

Counts

4 → 918

Calls

4 calls:

47.0ms	(/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t))))
145.0ms	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))
148.0ms	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))
148.0ms	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t))))
166.0ms	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))
170.0ms	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))
168.0ms	(+ x (/ (- y x) (/ (/ (- a t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt (- z t)))))

simplify250.0ms

Algorithm

egg-herbie

Counts

930 → 930

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	3783	22485
1	5002	22379

prune44.2s

Filtered

930 candidates to 546 candidates (41.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	927	3	930
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	928	14	942

Merged error: 6.0b

Counts

942 → 14

regimes664.0ms

Accuracy

2.1% (7.4b remaining)

Error of 11.5b against oracle of 4.2b and baseline of 11.7b

bsearch88.0ms

Steps

Iters	Range		Point
7	2.8066137419734734e-158	4.994043433676149e-157	7.017138754438094e-158
6	-2.3322346263693613e-256	-4.3653307229010104e-257	-2.3068432277006174e-256

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample920.0ms

Algorithm

intervals

Results

267.0ms	7780×	body	80	valid
65.0ms	495×	body	640	valid
43.0ms	265×	body	1280	valid
41.0ms	425×	body	320	valid
18.0ms	250×	body	160	valid
3.0ms	14×	body	2560	valid

Details

sample39.0ms

simplify60.0ms

prune5.0ms

localize9.0ms

rewrite29.0ms

series314.0ms

simplify52.0ms

prune458.0ms

localize9.0ms

rewrite79.0ms

series451.0ms

simplify112.0ms

prune2.2s

localize13.0ms

rewrite318.0ms

series737.0ms

simplify243.0ms

prune26.1s

localize22.0ms

rewrite603.0ms

series741.0ms

simplify250.0ms

prune44.2s

regimes664.0ms

bsearch88.0ms

simplify1.0ms

end0.0ms

sample920.0ms

end1.2m

Profiling