Details

analyze2.2s

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
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

sample100.0ms

Algorithm

intervals

Results

18.0ms	185×	body	80	valid
18.0ms	28×	body	640	valid
10.0ms	15×	body	1280	valid
9.0ms	88×	body	80	invalid
8.0ms	18×	body	640	invalid
6.0ms	18×	body	320	valid
4.0ms	6×	body	1280	invalid
2.0ms	10×	body	160	valid
2.0ms	5×	body	320	invalid
0.0ms	1×	body	160	invalid

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5091	32

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 40.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
37.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
98×	`associate-r/` `associate-l/`
73×	`cos-mult`
12×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `sqr-cos-a` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

4.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
141.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify106.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4972	11939
1	4972	11939

prune501.0ms

Filtered

138 candidates to 204 candidates (-47.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	196	8	204
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	196	9	205

Merged error: 25.1b

Counts

205 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
1.2b	(log (exp (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)))
3.6b	(cos (/ (+ phi1 phi2) 2.0))
37.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (log (exp (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `flip--`
80×	`associate-*l/`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
11×	`log-pow`
10×	`exp-prod`
7×	`pow1`
6×	`cbrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `log-prod` `sqrt-prod`
2×	`pow-pow` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `rem-log-exp` `pow-exp` `flip-+`

Counts

4 → 129

Calls

4 calls:

3.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
4.0ms	(log (exp (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (log (exp (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))))) (* (- phi1 phi2) (- phi1 phi2))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
22.0ms	(log (exp (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
137.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (log (exp (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4993	6218
1	4993	6218

prune331.0ms

Filtered

98 candidates to 141 candidates (-43.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	141	9	150

Merged error: 25.1b

Counts

150 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
3.6b	(cos (/ (+ phi1 phi2) 2.0))
5.9b	(exp (log (sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))))
37.3b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-*l/`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `exp-diff`
64×	`associate-*r/`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`unpow-prod-down` `log-prod` `exp-prod` `exp-sum` `sqrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `log-pow`
2×	`pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-exp` `rem-exp-log` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

3.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(exp (log (sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
137.0ms	(exp (log (sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))))
141.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

simplify73.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5026	11775

prune511.0ms

Filtered

136 candidates to 205 candidates (-50.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	200	5	205
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	201	13	214

Merged error: 25.1b

Counts

214 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
3.6b	(cos (/ (+ phi1 phi2) 2.0))
6.4b	(pow (exp 1/2) (log (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2)))))
38.8b	(log (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-*l/`
132×	`log-div`
128×	`frac-times` `frac-add`
66×	`pow-sub`
64×	`associate-*r/`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
8×	`pow1`
7×	`pow-unpow`
6×	`add-exp-log` `log-prod` `pow-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-up` `cbrt-prod` `exp-prod`
2×	`pow-to-exp` `flip3-+` `pow-exp` `log-pow` `flip-+` `sqr-pow`
1×	`pow1/3` `rem-log-exp`

Counts

4 → 196

Calls

4 calls:

3.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
23.0ms	(pow (exp 1/2) (log (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2)))))
18.0ms	(log (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
174.0ms	(pow (exp 1/2) (log (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2)))))
113.0ms	(log (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

simplify81.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5670	12673

prune545.0ms

Filtered

139 candidates to 208 candidates (-49.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	202	6	208
Fresh	1	9	10
Picked	1	0	1
Done	0	2	2
Total	204	17	221

Merged error: 22.2b

Counts

221 → 17

regimes1.1s

Accuracy

23.3% (15.4b remaining)

Error of 34.5b against oracle of 19.1b and baseline of 39.2b

bsearch168.0ms

Steps

Iters	Range	Point
7	6.152621355805654e-24	7.831252857443243e-22	2.1628661069747332e-23
10	1.8858009708456467e-152	1.5773965664601315e-136	8.893889606600523e-137
10	-1.3197293029156245e-39	-1.0307960393028758e-52	-5.1932364225039894e-40

Iters

Range

Point

6.152621355805654e-24

7.831252857443243e-22

2.1628661069747332e-23

1.8858009708456467e-152

1.5773965664601315e-136

8.893889606600523e-137

-1.3197293029156245e-39

-1.0307960393028758e-52

-5.1932364225039894e-40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	107	108
1	107	108

end0.0ms

sample3.0s

Algorithm

intervals

Results

621.0ms	5905×	body	80	valid
444.0ms	2313×	body	80	invalid
414.0ms	865×	body	640	valid
337.0ms	460×	body	1280	valid
211.0ms	458×	body	640	invalid
196.0ms	286×	body	1280	invalid
174.0ms	508×	body	320	valid
80.0ms	234×	body	320	invalid
63.0ms	262×	body	160	valid
25.0ms	102×	body	160	invalid

Details

analyze2.2s

sample100.0ms

simplify102.0ms

prune12.0ms

localize18.0ms

rewrite60.0ms

series159.0ms

simplify106.0ms

prune501.0ms

localize24.0ms

rewrite40.0ms

series187.0ms

simplify64.0ms

prune331.0ms

localize25.0ms

rewrite71.0ms

series305.0ms

simplify73.0ms

prune511.0ms

localize30.0ms

rewrite69.0ms

series312.0ms

simplify81.0ms

prune545.0ms

regimes1.1s

bsearch168.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling