Details

Time bar (total: 26.4s)

sample521.0ms

Algorithm
intervals
Results
193.0ms33×body5120valid
141.0ms72×body2560valid
96.0ms122×body1280valid
44.0ms87×body640valid
12.0ms32×body320valid
7.0ms59×body80valid
6.0ms14×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114713
285712
3500211

prune12.0ms

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: 39.1b

Counts
2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
1.3b
(* (pow t 3.0) (tan k))
17.2b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.8b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
392×add-exp-log
265×prod-exp
74×div-exp add-cbrt-cube
61×pow-exp
41×pow-to-exp
40×cbrt-unprod
25×associate-*l*
21×add-sqr-sqrt
17×unpow-prod-down
16×add-cube-cbrt *-un-lft-identity
12×cbrt-undiv
10×times-frac
7×associate-*r/ associate-*r*
6×pow1
4×tan-quot add-log-exp
3×*-commutative unswap-sqr sqr-pow
2×associate-*l/ div-inv
1×frac-2neg pow-prod-down clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 185
Calls
4 calls:
12.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
263.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
237.0ms
(* (pow t 3.0) (tan k))
360.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
241.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify132.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09082174
147741790
250021790

prune374.0ms

Filtered
197 candidates to 80 candidates (40.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1898197
Fresh101
Picked101
Done000
Total1918199

Merged error: 18.6b

Counts
199 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.4b
(* (pow k 2.0) (pow t 1.0))
13.4b
(* (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:
335.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
324.0ms
(* (pow k 2.0) (pow t 1.0))
646.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify161.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
013167192
141627023
250027016

prune546.0ms

Filtered
612 candidates to 99 candidates (16.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New6048612
Fresh257
Picked101
Done000
Total60713620

Merged error: 15.5b

Counts
620 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.4b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.4b
(* (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)))

rewrite276.0ms

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))
41.0ms
(* (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)
337.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
646.0ms
(* (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)))

simplify296.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
0174223541
1457419109
2500217856

prune705.0ms

Filtered
1472 candidates to 86 candidates (5.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New146751472
Fresh4812
Picked101
Done000
Total1472131485

Merged error: 11.4b

Counts
1485 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
2.1b
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
4.9b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.7b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
25023×add-exp-log
19197×prod-exp
16899×pow-exp
11140×div-exp
7959×pow-to-exp
2990×rec-exp 1-exp
51×unpow-prod-down
43×times-frac
40×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r* sqr-pow
8×cbrt-undiv
5×pow1 div-inv
4×associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 5762
Calls
4 calls:
7.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
107.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
23.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
333.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
631.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
629.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Algorithm
egg-herbie
Counts
5774 → 5774
Iterations

Useful iterations: 1 (66.0ms)

IterNodesCost
04423106445
15002106271

prune733.0ms

Filtered
5774 candidates to 117 candidates (2.0%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New576865774
Fresh3912
Picked101
Done000
Total5772155787

Merged error: 11.4b

Counts
5787 → 15

regimes382.0ms

Accuracy

44.1% (2.9b remaining)

Error of 16.2b against oracle of 13.4b and baseline of 18.5b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05043
15043

end0.0ms

sample14.4s

Algorithm
intervals
Results
4.5s2211×body2560valid
4.1s943×body5120valid
3.2s4098×body1280valid
1.3s2517×body640valid
514.0ms985×body320valid
260.0ms2010×body80valid
111.0ms429×body160valid

Profiling

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