Details

Time bar (total: 18.2s)

sample134.0ms

Algorithm
intervals
Results
43.0ms54×body1280valid
38.0ms65×body640valid
19.0ms178×body80valid
10.0ms27×body320valid
5.0ms20×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04813
116113
294413
3500212

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.8b

localize20.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
4.1b
(* (pow t 3.0) (sin k))
7.1b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
25.1b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
73×times-frac
56×add-sqr-sqrt
50×div-exp
41×add-cube-cbrt *-un-lft-identity
40×prod-exp
33×associate-*l*
30×cbrt-undiv
22×cbrt-unprod
11×div-inv
10×associate-*r*
8×associate-/l*
7×unswap-sqr
6×pow1 associate-/r*
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative sqr-pow
1×frac-times associate-*r/ pow-prod-down associate-*l/ associate-/l/
Counts
4 → 184
Calls
4 calls:
20.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
15.0ms
(* (pow t 3.0) (sin k))
9.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
61.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
310.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
155.0ms
(* (pow t 3.0) (sin k))
68.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
809.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify44.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010192396
150011978

prune733.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.3b

localize24.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
4.1b
(* (pow t 3.0) (sin k))
5.8b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
16.4b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
49×prod-exp
41×div-exp
33×add-sqr-sqrt
27×cbrt-unprod
25×cbrt-undiv
22×associate-*l*
21×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
8×pow1
6×unswap-sqr
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-/r* *-commutative
2×tan-quot pow-prod-down associate-/r/ sqr-pow
1×frac-times frac-2neg associate-*r/ clear-num associate-/l/ associate-/l*
Counts
4 → 150
Calls
4 calls:
26.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
13.0ms
(* (pow t 3.0) (sin k))
32.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
88.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
432.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
153.0ms
(* (pow t 3.0) (sin k))
317.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
815.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify119.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09131905
148941506
250011506

prune576.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.5b

localize23.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.3b
(/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k))
8.9b
(* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))
16.4b
(* (/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
480×add-exp-log
225×prod-exp
202×div-exp
104×pow-exp
95×add-sqr-sqrt
76×times-frac
70×add-cbrt-cube
52×unpow-prod-down
51×*-un-lft-identity
45×add-cube-cbrt
37×associate-*l*
32×pow-to-exp
27×cbrt-unprod
26×associate-*r*
24×rec-exp 1-exp
22×cbrt-undiv
20×unswap-sqr
10×sqr-pow
6×pow1 associate-/r* div-inv
4×expm1-log1p-u associate-*r/ log1p-expm1-u associate-/l* add-log-exp
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative
1×frac-times pow-prod-down associate-*l/ associate-/l/
Counts
4 → 278
Calls
4 calls:
5.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
58.0ms
(/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k))
56.0ms
(* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))
191.0ms
(* (/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
380.0ms
(/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k))
234.0ms
(* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))
840.0ms
(* (/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify61.0ms

Algorithm
egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013973722
150013275

prune915.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.7b

localize45.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))
2.9b
(* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k)))
3.3b
(/ (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k))
16.4b
(* (/ (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
3945×add-exp-log
2148×prod-exp
1537×div-exp
1126×pow-exp
336×pow-to-exp
153×add-sqr-sqrt
148×unpow-prod-down
129×times-frac
98×add-cbrt-cube
89×associate-*l*
73×*-un-lft-identity
70×cbrt-prod
65×add-cube-cbrt
46×cbrt-unprod
32×unswap-sqr
27×associate-*r*
26×cbrt-undiv
17×sqr-pow
7×associate-*r/
6×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
2×tan-quot associate-/r/
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num associate-/l/ associate-/l*
Counts
4 → 819
Calls
4 calls:
113.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))
98.0ms
(* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k)))
280.0ms
(/ (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k))
978.0ms
(* (/ (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
284.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))
278.0ms
(* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k)))
434.0ms
(/ (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k))
644.0ms
(* (/ (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow (* (cbrt t) (cbrt t)) 3.0)) 1.0) (* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k))))) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify196.0ms

Algorithm
egg-herbie
Counts
831 → 831
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0290719000
1500118352

prune1.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 20.0b

regimes884.0ms

Accuracy

0% (2.6b remaining)

Error of 22.8b against oracle of 20.2b and baseline of 22.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03834
13834

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2043×body1280valid
905.0ms1700×body640valid
680.0ms5869×body80valid
329.0ms858×body320valid
126.0ms473×body160valid