Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

sample30.0ms

Algorithm

intervals

Results

8.0ms	209×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	33×	body	80	invalid
1.0ms	7×	body	1280	valid
0.0ms	2×	body	2560	valid
0.0ms	3×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

prune14.0ms

Filtered

1 candidates to 1 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: 11.2b

Counts

2 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.3b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.0b	(* (- y x) (/ (- z t) (- a t)))

rewrite39.0ms

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:

7.0ms	(/ (- z t) (- a t))
4.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
22.0ms	(* (- y x) (/ (- z t) (- a t)))

series100.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ (- z t) (- a t))
57.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
34.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify43.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5068	1606

prune187.0ms

Filtered

87 candidates to 128 candidates (-47.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	116	12	128
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	116	14	130

Merged error: 3.2b

Counts

130 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- y x))
0.9b	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ (- z t) (- a t)) (cbrt (- y x))))
1.4b	(* (/ (- z t) (- a t)) (cbrt (- y x)))
8.1b	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ (- z t) (- a t)) (cbrt (- y x)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

114×	`cbrt-div`
84×	`frac-times`
58×	`flip3--` `flip--`
52×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
37×	`associate-*r/`
32×	`associate-l`
30×	`add-exp-log` `associate-*l/`
27×	`times-frac`
18×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
15×	`prod-exp` `cbrt-unprod`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
9×	`associate-r` `pow-prod-down`
6×	`add-log-exp`
4×	`unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`associate-/r/` `*-commutative`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+` `div-inv`

Counts

4 → 166

Calls

4 calls:

3.0ms	(cbrt (- y x))
24.0ms	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ (- z t) (- a t)) (cbrt (- y x))))
19.0ms	(* (/ (- z t) (- a t)) (cbrt (- y x)))
4.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ (- z t) (- a t)) (cbrt (- y x)))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- y x))
36.0ms	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ (- z t) (- a t)) (cbrt (- y x))))
47.0ms	(* (/ (- z t) (- a t)) (cbrt (- y x)))
58.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ (- z t) (- a t)) (cbrt (- y x)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5028	3757

prune231.0ms

Filtered

108 candidates to 178 candidates (-64.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	177	15	192

Merged error: 3.2b

Counts

192 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- y x))
0.8b	(* (cbrt (- y x)) (/ (- z t) (cbrt (- a t))))
0.9b	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- y x)) (/ (- z t) (cbrt (- a t))))))
7.1b	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- y x)) (/ (- z t) (cbrt (- a t)))))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

233×	`add-exp-log`
224×	`cbrt-div`
219×	`frac-times`
156×	`prod-exp`
112×	`flip3--` `flip--`
99×	`associate-*r/`
79×	`associate-*l/`
72×	`add-sqr-sqrt`
68×	`cbrt-unprod`
60×	`add-cbrt-cube`
56×	`*-un-lft-identity`
47×	`associate-r`
44×	`times-frac`
40×	`cbrt-prod`
39×	`div-exp`
27×	`pow1`
26×	`add-cube-cbrt`
19×	`cbrt-undiv`
16×	`pow-prod-down`
15×	`distribute-lft-out--` `difference-of-squares`
12×	`rec-exp` `1-exp`
9×	`associate-l`
6×	`add-log-exp` `unswap-sqr`
2×	`associate-/r/` `*-commutative`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+` `div-inv`

Counts

4 → 291

Calls

4 calls:

3.0ms	(cbrt (- y x))
22.0ms	(* (cbrt (- y x)) (/ (- z t) (cbrt (- a t))))
46.0ms	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- y x)) (/ (- z t) (cbrt (- a t))))))
6.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- y x)) (/ (- z t) (cbrt (- a t)))))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- y x))
172.0ms	(* (cbrt (- y x)) (/ (- z t) (cbrt (- a t))))
46.0ms	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- y x)) (/ (- z t) (cbrt (- a t))))))
57.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (cbrt (- y x)) (/ (- z t) (cbrt (- a t)))))))

simplify76.0ms

Algorithm

egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5044	8716

prune330.0ms

Filtered

170 candidates to 303 candidates (-78.2%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	299	4	303
Fresh	4	8	12
Picked	0	1	1
Done	0	2	2
Total	303	15	318

Merged error: 3.2b

Counts

318 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- y x))
0.7b	(cbrt (- y x))
0.9b	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (* (cbrt (- y x)) (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (cbrt (- a t))))))
7.3b	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (* (cbrt (- y x)) (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (cbrt (- a t)))))))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

3244×	`cbrt-div`
3241×	`frac-times`
1622×	`flip3--` `flip--`
1322×	`associate-*r/`
989×	`associate-*l/`
632×	`add-exp-log`
458×	`prod-exp`
194×	`cbrt-unprod`
132×	`add-cbrt-cube`
98×	`div-exp`
49×	`pow1`
46×	`cbrt-undiv`
35×	`pow-prod-down`
28×	`rec-exp` `1-exp`
10×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
2×	`pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `associate-r` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

4 → 1176

Calls

4 calls:

3.0ms	(cbrt (- y x))
3.0ms	(cbrt (- y x))
96.0ms	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (* (cbrt (- y x)) (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (cbrt (- a t))))))
8.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (* (cbrt (- y x)) (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (cbrt (- a t)))))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- y x))
28.0ms	(cbrt (- y x))
47.0ms	(* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (* (cbrt (- y x)) (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (cbrt (- a t))))))
63.0ms	(+ x (* (* (cbrt (- y x)) (cbrt (- y x))) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (* (* (cbrt (- y x)) (* (cbrt (- z t)) (cbrt (- z t)))) (/ (cbrt (- z t)) (cbrt (- a t)))))))

simplify407.0ms

Algorithm

egg-herbie

Counts

1188 → 1188

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5764	89673

prune4.0s

Filtered

1073 candidates to 1188 candidates (-10.7%)

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	1188	0	1188
Fresh	0	11	11
Picked	0	1	1
Done	0	3	3
Total	1188	15	1203

Merged error: 3.2b

Counts

1203 → 15

regimes808.0ms

Accuracy

23.9% (6.4b remaining)

Error of 10.1b against oracle of 3.7b and baseline of 12.1b

bsearch49.0ms

Steps

Iters	Range		Point
7	5.240519896804567e+150	1.1478145782376848e+152	1.0148871718215874e+152
10	-8.213621294406486e+132	-6.878983873000893e+115	-1.7069872670333652e+128

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	35
1	82	35

end0.0ms

sample784.0ms

Algorithm

intervals

Results

253.0ms	6496×	body	80	valid
76.0ms	488×	body	640	valid
54.0ms	292×	body	1280	valid
46.0ms	440×	body	320	valid
44.0ms	1199×	body	80	invalid
19.0ms	264×	body	160	valid
4.0ms	20×	body	2560	valid

Details

analyze1.1s

sample30.0ms

simplify53.0ms

prune14.0ms

localize9.0ms

rewrite39.0ms

series100.0ms

simplify43.0ms

prune187.0ms

localize13.0ms

rewrite62.0ms

series169.0ms

simplify44.0ms

prune231.0ms

localize19.0ms

rewrite101.0ms

series304.0ms

simplify76.0ms

prune330.0ms

localize23.0ms

rewrite355.0ms

series165.0ms

simplify407.0ms

prune4.0s

regimes808.0ms

bsearch49.0ms

simplify2.0ms

end0.0ms

sample784.0ms

Profiling