Details

Time bar (total: 24.9s)

sample509.0ms

Algorithm
intervals
Results
168.0ms82×body2560valid
157.0ms38×body5120valid
90.0ms118×body1280valid
44.0ms89×body640valid
13.0ms39×body320valid
8.0ms65×body80valid
5.0ms23×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04413
114713
285712
3500211

prune11.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.8b
(* (pow t 3.0) (tan k))
21.6b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.6b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
337×add-exp-log
220×prod-exp
71×div-exp
65×add-cbrt-cube
51×pow-exp
34×pow-to-exp cbrt-unprod
30×unpow-prod-down
28×add-sqr-sqrt
24×associate-*l*
23×add-cube-cbrt *-un-lft-identity
19×times-frac
12×cbrt-undiv
5×pow1 associate-*r/
4×associate-*r* add-log-exp sqr-pow
3×tan-quot pow-unpow div-inv unswap-sqr
2×*-commutative
1×pow-pow frac-2neg associate-*l/ clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 179
Calls
4 calls:
5.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
22.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series922.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(pow (/ k t) 2.0)
240.0ms
(* (pow t 3.0) (tan k))
364.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
250.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify140.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09741954
149951620
250011620

prune463.0ms

Filtered
191 candidates to 88 candidates (46.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.8b
(* (pow k 2.0) (pow t 1.0))
17.5b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
1645×add-exp-log
1122×prod-exp
899×pow-exp
688×div-exp
509×pow-to-exp
140×rec-exp 1-exp
37×add-sqr-sqrt
29×unpow-prod-down
25×add-cbrt-cube
22×times-frac
20×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×associate-*l*
13×sqr-pow
12×unswap-sqr
9×associate-/r*
7×cbrt-unprod
6×cbrt-undiv
5×pow1
4×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
Calls
4 calls:
7.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
12.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms
(* (pow k 2.0) (pow t 1.0))
21.0ms
(* (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:
333.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
83.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
330.0ms
(* (pow k 2.0) (pow t 1.0))
641.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify156.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
013167194
141627025
250027018

prune599.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.5b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1460
Calls
4 calls:
2.0ms
(pow (sin k) 2)
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
34.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (sin k) 2)
346.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
662.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify288.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune554.0ms

Filtered
1472 candidates to 86 candidates (5.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 14.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos k) (sin k))
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.2b
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
17.5b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
3841×add-exp-log
2622×prod-exp
1370×div-exp
1330×pow-exp
679×pow-to-exp
248×rec-exp 1-exp
99×times-frac
80×add-sqr-sqrt
65×add-cbrt-cube
59×add-cube-cbrt *-un-lft-identity
45×associate-*r*
24×associate-*l*
22×cbrt-undiv cbrt-unprod
8×div-inv
7×pow1 unpow-prod-down
6×associate-/l* unswap-sqr
5×associate-*r/
4×associate-/r* add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip pow-prod-down associate-/r/ inv-pow sqr-pow
Counts
4 → 931
Calls
4 calls:
4.0ms
(/ (cos k) (sin k))
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
20.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
236.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (cos k) (sin k))
336.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
647.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify166.0ms

Algorithm
egg-herbie
Counts
943 → 943
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0214715097
1500212259

prune718.0ms

Filtered
943 candidates to 133 candidates (14.1%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

regimes383.0ms

Accuracy

46.6% (3.7b remaining)

Error of 12.2b against oracle of 8.5b and baseline of 15.4b

bsearch1.7s

Steps
ItersRangePoint
6
5.0665987669896065e+270
6.21352233526469e+271
2.8268215145376105e+271
6
1.0610438957915185e+118
1.220354401717147e+119
1.1985389443281593e+119
9
3.842300563538073e-125
1.6022377675487767e-119
2.2900022502019674e-123
10
-1.6345552968471917e-121
-4.059779562671444e-140
-8.813192694035889e-140
7
-2.1532264321590984e+161
-6.625721383123302e+159
-6.6947721379174745e+159

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
081107
181107

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.4s2270×body2560valid
3.9s956×body5120valid
3.1s4060×body1280valid
1.3s2537×body640valid
370.0ms1015×body320valid
247.0ms2050×body80valid
111.0ms448×body160valid