Details

Time bar (total: 29.4s)

sample460.0ms

Algorithm
intervals
Results
138.0ms36×body5120valid
126.0ms68×body2560valid
109.0ms132×body1280valid
40.0ms79×body640valid
11.0ms30×body320valid
8.0ms67×body80valid
6.0ms26×body160valid

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (25.0ms)

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)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 42.1b

Counts
2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.8b
(* (pow t 3.0) (tan k))
24.0b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.0b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite51.0ms

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))
18.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
12.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series894.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ k t) 2.0)
232.0ms
(* (pow t 3.0) (tan k))
359.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
243.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify142.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09741954
149951620
250011620

prune421.0ms

Filtered
191 candidates to 88 candidates (46.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New18011191
Fresh011
Picked101
Done000
Total18112193

Merged error: 24.6b

Counts
193 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.7b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.9b
(* (pow k 2.0) (pow t 1.0))
18.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite103.0ms

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)))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms
(* (pow k 2.0) (pow t 1.0))
22.0ms
(* (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)))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
327.0ms
(* (pow k 2.0) (pow t 1.0))
626.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify159.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
013167194
141627025
250027018

prune576.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New59913612
Fresh8311
Picked101
Done000
Total60816624

Merged error: 19.9b

Counts
624 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.7b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.4b
(* (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)))

rewrite275.0ms

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:
3.0ms
(pow (sin k) 2)
17.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
9.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
39.0ms
(* (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)
336.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
639.0ms
(* (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)))

simplify518.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune517.0ms

Filtered
1472 candidates to 86 candidates (5.8%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New146481472
Fresh6915
Picked101
Done000
Total1471171488

Merged error: 15.7b

Counts
1488 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos k) (/ (/ (sin k) l) l))
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.4b
(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
18.4b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

rewrite447.0ms

Algorithm
rewrite-expression-head
Rules
3522×times-frac
2743×add-exp-log
1561×add-sqr-sqrt
1506×add-cube-cbrt *-un-lft-identity prod-exp
1348×div-exp
974×pow-exp
509×pow-to-exp
406×associate-*r*
186×rec-exp 1-exp
140×associate-/l*
112×div-inv
56×add-cbrt-cube
47×associate-/r*
29×cbrt-undiv
15×unswap-sqr
12×unpow-prod-down
11×associate-*l*
8×associate-/r/ cbrt-unprod
6×sqr-pow
5×pow1
4×add-log-exp
3×frac-2neg clear-num
1×pow-flip associate-*r/ *-commutative associate-/l/ inv-pow
Counts
4 → 1791
Calls
4 calls:
14.0ms
(/ (cos k) (/ (/ (sin k) l) l))
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
42.0ms
(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
164.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

series1.2s

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (cos k) (/ (/ (sin k) l) l))
336.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms
(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
654.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

simplify345.0ms

Algorithm
egg-herbie
Counts
1803 → 1803
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500134093

prune6.4s

Filtered
1803 candidates to 1141 candidates (63.3%)
Pruning

21 alts after pruning (20 fresh and 1 done)

PrunedKeptTotal
New1788151803
Fresh11516
Picked011
Done000
Total1799211820

Merged error: 10.0b

Counts
1820 → 21

regimes547.0ms

Accuracy

49.9% (2.6b remaining)

Error of 10.3b against oracle of 7.7b and baseline of 12.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06572
16572

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.6s2260×body2560valid
3.6s887×body5120valid
3.1s4018×body1280valid
1.3s2496×body640valid
383.0ms1001×body320valid
275.0ms2017×body80valid
113.0ms457×body160valid