Details

Time bar (total: 22.5s)

sample424.0ms

Algorithm
intervals
Results
130.0ms34×body5120valid
118.0ms71×body2560valid
87.0ms129×body1280valid
45.0ms92×body640valid
11.0ms35×body320valid
7.0ms64×body80valid
3.0ms13×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111

prune11.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.0b

Counts
2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
20.1b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.5b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
54×associate-*l*
38×associate-*r* *-commutative
36×times-frac
14×sqr-pow
9×associate-/r*
8×div-inv
7×unpow-prod-down
5×associate-*r/
4×associate-/l*
3×tan-quot
1×pow-to-exp frac-2neg associate-*l/ clear-num associate-/r/
Counts
4 → 66
Calls
4 calls:
2.0ms
(pow (/ k t) 2.0)
4.0ms
(* (pow t 3.0) (tan k))
11.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
7.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series895.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ k t) 2.0)
231.0ms
(* (pow t 3.0) (tan k))
358.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
242.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify50.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0478690
11920679
25001679

prune291.0ms

Filtered
78 candidates to 63 candidates (80.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New70878
Fresh101
Picked101
Done000
Total72880

Merged error: 14.5b

Counts
80 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.6b
(* (pow k 2.0) (pow t 1.0))
16.1b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×sqr-pow
23×associate-*r*
16×times-frac unpow2
9×associate-*r/ associate-/r* *-commutative
8×associate-/l*
4×pow-to-exp associate-*l* clear-num div-inv
3×frac-2neg
2×prod-exp unswap-sqr
1×unpow-prod-down rec-exp un-div-inv inv-pow
Counts
4 → 54
Calls
4 calls:
5.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
7.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.0ms
(* (pow k 2.0) (pow t 1.0))
12.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
328.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
322.0ms
(* (pow k 2.0) (pow t 1.0))
630.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify38.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0495549
11213547
25002547

prune317.0ms

Filtered
66 candidates to 51 candidates (77.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New58866
Fresh257
Picked101
Done000
Total611374

Merged error: 9.7b

Counts
74 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ (pow (sin k) 2) l)
4.3b
(/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (/ (pow (sin k) 2) l))
6.6b
(* (pow k 2.0) (pow t 1.0))
7.2b
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l*
12×div-inv
10×associate-/l*
9×sqr-pow
7×*-commutative
6×times-frac
5×associate-/r/
3×unpow-prod-down frac-2neg clear-num
2×pow-to-exp unpow2
1×associate-*r* prod-exp associate-/r* unswap-sqr
Counts
4 → 36
Calls
4 calls:
3.0ms
(/ (pow (sin k) 2) l)
11.0ms
(/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (/ (pow (sin k) 2) l))
4.0ms
(* (pow k 2.0) (pow t 1.0))
8.0ms
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)

series1.4s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (pow (sin k) 2) l)
648.0ms
(/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (/ (pow (sin k) 2) l))
331.0ms
(* (pow k 2.0) (pow t 1.0))
373.0ms
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)

simplify38.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0369441
11231435
25002433

prune263.0ms

Filtered
48 candidates to 40 candidates (83.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New43548
Fresh3912
Picked101
Done000
Total471461

Merged error: 8.7b

Counts
61 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.1b
(/ (pow (sin k) 2) l)
4.3b
(/ (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (cos k)) l) (/ (pow (sin k) 2) l))
7.2b
(* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (cos k)) l)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*l*
13×div-inv sqr-pow
10×associate-/r* associate-/l*
8×*-commutative
6×times-frac associate-*r*
5×associate-/r/
4×frac-2neg clear-num
3×pow-to-exp unpow-prod-down unswap-sqr
2×prod-exp unpow2
1×rec-exp inv-pow
Counts
4 → 45
Calls
4 calls:
10.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.0ms
(/ (pow (sin k) 2) l)
16.0ms
(/ (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (cos k)) l) (/ (pow (sin k) 2) l))
13.0ms
(* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (cos k)) l)

series1.4s

Counts
4 → 12
Calls
4 calls:
344.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
42.0ms
(/ (pow (sin k) 2) l)
651.0ms
(/ (* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (cos k)) l) (/ (pow (sin k) 2) l))
372.0ms
(* (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (cos k)) l)

simplify46.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0431577
11533482
25001480

prune259.0ms

Filtered
57 candidates to 50 candidates (87.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New52557
Fresh5813
Picked101
Done000
Total581371

Merged error: 7.5b

Counts
71 → 13

regimes316.0ms

Accuracy

25.5% (1.9b remaining)

Error of 10.6b against oracle of 8.7b and baseline of 11.2b

bsearch1.2s

Steps
ItersRangePoint
4
7.723717393936413e+80
1.182396247124819e+81
1.090799127848314e+81
7
6.800262453525831e-20
7.687332883799488e-18
1.4658926919355537e-19
7
-5.332596795476241e-36
-8.588094909214782e-38
-5.807125110739911e-37
9
-1.0189745070055278e+128
-2.2118801766293464e+120
-2.2439854096143383e+120

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07287
17487
27487

end0.0ms

sample14.0s

Algorithm
intervals
Results
4.4s2264×body2560valid
4.3s952×body5120valid
3.0s4101×body1280valid
1.2s2475×body640valid
354.0ms1013×body320valid
237.0ms2086×body80valid
101.0ms432×body160valid