Details

analyze986.0ms

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
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

sample27.0ms

Algorithm

intervals

Results

8.0ms	221×	body	80	valid
2.0ms	11×	body	640	valid
1.0ms	18×	body	80	invalid
1.0ms	5×	body	1280	valid
1.0ms	11×	body	160	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	2560	valid

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4893	13
1	4893	13

prune13.0ms

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: 5.3b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ y (* y (/ (- z t) (- t a)))))
0.0b	(/ (- z t) (- t a))
2.5b	(+ y (* y (/ (- z t) (- t a))))
2.8b	(* y (/ (- z t) (- t a)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

5.0ms	(+ x (+ y (* y (/ (- z t) (- t a)))))
8.0ms	(/ (- z t) (- t a))
3.0ms	(+ y (* y (/ (- z t) (- t a))))
18.0ms	(* y (/ (- z t) (- t a)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ x (+ y (* y (/ (- z t) (- t a)))))
9.0ms	(/ (- z t) (- t a))
21.0ms	(+ y (* y (/ (- z t) (- t a))))
15.0ms	(* y (/ (- z t) (- t a)))

simplify43.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5072	1615

prune165.0ms

Filtered

96 candidates to 139 candidates (-44.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	130	9	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Merged error: 3.0b

Counts

141 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

2.5b	(+ y (* y (/ (- z t) (- t a))))
2.8b	(* y (/ (- z t) (- t a)))
2.8b	(* y (/ (- z t) (- t a)))
2.8b	(* y (/ (- z t) (- t a)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
93×	`associate-r`
78×	`times-frac`
40×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
19×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
6×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 161

Calls

4 calls:

3.0ms	(+ y (* y (/ (- z t) (- t a))))
14.0ms	(* y (/ (- z t) (- t a)))
15.0ms	(* y (/ (- z t) (- t a)))
17.0ms	(* y (/ (- z t) (- t a)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ y (* y (/ (- z t) (- t a))))
19.0ms	(* y (/ (- z t) (- t a)))
16.0ms	(* y (/ (- z t) (- t a)))
16.0ms	(* y (/ (- z t) (- t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5487	1727

prune186.0ms

Filtered

114 candidates to 173 candidates (-51.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	172	10	182

Merged error: 3.0b

Counts

182 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(+ y (* y (/ (- z t) (- t a))))
2.8b	(* y (/ (- z t) (- t a)))
2.8b	(* y (/ (- z t) (- t a)))
12.8b	(+ y (* (* (cbrt y) (cbrt y)) (* (/ (- z t) (- t a)) (cbrt y))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
62×	`associate-r`
52×	`times-frac`
29×	`add-cube-cbrt`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `add-log-exp`
6×	`associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `flip3--` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip--` `flip-+` `div-inv`
1×	`distribute-lft-out`

Counts

4 → 123

Calls

4 calls:

3.0ms	(+ y (* y (/ (- z t) (- t a))))
15.0ms	(* y (/ (- z t) (- t a)))
14.0ms	(* y (/ (- z t) (- t a)))
4.0ms	(+ y (* (* (cbrt y) (cbrt y)) (* (/ (- z t) (- t a)) (cbrt y))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ y (* y (/ (- z t) (- t a))))
15.0ms	(* y (/ (- z t) (- t a)))
15.0ms	(* y (/ (- z t) (- t a)))
32.0ms	(+ y (* (* (cbrt y) (cbrt y)) (* (/ (- z t) (- t a)) (cbrt y))))

simplify43.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5171	1418

prune156.0ms

Filtered

93 candidates to 135 candidates (-45.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	135	10	145

Merged error: 3.0b

Counts

145 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

2.8b	(* y (/ (- z t) (- t a)))
2.8b	(* y (/ (- z t) (- t a)))
7.0b	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a))))
11.2b	(+ y (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

141×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
108×	`associate-r`
102×	`times-frac`
49×	`add-cube-cbrt`
35×	`add-exp-log`
33×	`distribute-lft-out--` `difference-of-squares`
28×	`add-cbrt-cube`
27×	`cbrt-prod`
21×	`associate-l`
14×	`cbrt-div` `associate-/r/`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1` `unswap-sqr`
9×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`add-log-exp`
5×	`frac-times` `associate-*r/`
4×	`div-inv`
3×	`pow-prod-down` `associate-l/` `-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 202

Calls

4 calls:

14.0ms	(* y (/ (- z t) (- t a)))
14.0ms	(* y (/ (- z t) (- t a)))
34.0ms	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a))))
6.0ms	(+ y (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a)))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* y (/ (- z t) (- t a)))
15.0ms	(* y (/ (- z t) (- t a)))
22.0ms	(* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a))))
28.0ms	(+ y (* (/ y (* (cbrt (- t a)) (cbrt (- t a)))) (/ (- z t) (cbrt (- t a)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5018	2963

prune191.0ms

Filtered

146 candidates to 214 candidates (-46.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	214	10	224

Merged error: 3.0b

Counts

224 → 10

regimes538.0ms

Accuracy

1.5% (4.4b remaining)

Error of 7.7b against oracle of 3.3b and baseline of 7.8b

bsearch86.0ms

Steps

Iters	Range		Point
7	5.59961110125984e+275	5.3242148228800254e+277	3.311116811777091e+277
10	3.649876644803024e+140	3.3617830896860006e+159	3.021594397083245e+158
5	4.339641137108113e-305	1.3798554742892508e-304	1.3569370442215147e-304
10	-5.4511565935899955e-36	-1.1096317743480614e-50	-1.960689538275324e-45

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	133
1	75	133

end0.0ms

sample766.0ms

Algorithm

intervals

Results

273.0ms	6653×	body	80	valid
67.0ms	438×	body	640	valid
50.0ms	255×	body	1280	valid
46.0ms	394×	body	320	valid
26.0ms	690×	body	80	invalid
18.0ms	244×	body	160	valid
3.0ms	16×	body	2560	valid

Details

analyze986.0ms

sample27.0ms

simplify93.0ms

prune13.0ms

localize9.0ms

rewrite39.0ms

series81.0ms

simplify43.0ms

prune165.0ms

localize14.0ms

rewrite57.0ms

series72.0ms

simplify55.0ms

prune186.0ms

localize26.0ms

rewrite41.0ms

series84.0ms

simplify43.0ms

prune156.0ms

localize23.0ms

rewrite80.0ms

series82.0ms

simplify58.0ms

prune191.0ms

regimes538.0ms

bsearch86.0ms

simplify2.0ms

end0.0ms

sample766.0ms

Profiling