Details

Time bar (total: 28.9s)

sample494.0ms

Algorithm
intervals
Results
146.0ms73×body2560valid
137.0ms132×body1280valid
101.0ms25×body5120valid
64.0ms86×body640valid
13.0ms26×body320valid
8.0ms46×body80valid
4.0ms12×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114713
285712
3500211

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.8b
(* (pow t 3.0) (tan k))
19.0b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.5b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite86.0ms

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:
3.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
42.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
24.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series891.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ k t) 2.0)
237.0ms
(* (pow t 3.0) (tan k))
357.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
238.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify135.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09741954
149951620
250011620

prune434.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.8b
(* (pow k 2.0) (pow t 1.0))
15.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite113.0ms

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)))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms
(* (pow k 2.0) (pow t 1.0))
33.0ms
(* (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:
326.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
84.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
319.0ms
(* (pow k 2.0) (pow t 1.0))
637.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify151.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
013167194
141627025
250027018

prune605.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
0.5b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.4b
(* (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)))

rewrite296.0ms

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:
1.0ms
(pow (sin k) 2)
21.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
61.0ms
(* (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:
18.0ms
(pow (sin k) 2)
338.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
643.0ms
(* (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)))

simplify279.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune558.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos k) (fabs (sin k)))
0.5b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.2b
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
15.4b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

rewrite457.0ms

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:
3.0ms
(/ (cos k) (fabs (sin k)))
20.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
235.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
60.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series1000.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (cos k) (fabs (sin k)))
320.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
69.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
594.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify166.0ms

Algorithm
egg-herbie
Counts
943 → 943
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0215016793
1500113902

prune749.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.1b

regimes323.0ms

Accuracy

59.2% (2.8b remaining)

Error of 11.4b against oracle of 8.6b and baseline of 15.4b

bsearch2.8s

Steps
ItersRangePoint
8
3.1381575881074073e+153
4.745240176690994e+156
1.2218151027611354e+154
9
2.7413777313647e-155
9.0664153968876e-147
3.3090433695573168e-155
11
-1.637494300424913e-145
-2.849757602576434e-180
-5.157297826678039e-154
8
-3.104877055821389e+150
-1.0625869734742917e+147
-6.239143455459081e+149

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076101
176101

end0.0ms

sample16.9s

Algorithm
intervals
Results
5.0s2202×body2560valid
4.4s963×body5120valid
4.2s4069×body1280valid
1.8s2501×body640valid
521.0ms987×body320valid
368.0ms2020×body80valid
147.0ms426×body160valid