Details

Time bar (total: 17.8s)

sample140.0ms

Algorithm
intervals
Results
55.0ms70×body1280valid
31.0ms60×body640valid
24.0ms193×body80valid
10.0ms28×body320valid
3.0ms12×body160valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.5b

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow t 3.0) (sin k))
3.0b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
4.6b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
24.1b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite54.0ms

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:
6.0ms
(* (pow t 3.0) (sin k))
8.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
3.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
29.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (pow t 3.0) (sin k))
325.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
73.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
873.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010192396
150011978

prune750.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.9b

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow t 3.0) (sin k))
3.5b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
5.0b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
16.2b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite82.0ms

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:
6.0ms
(* (pow t 3.0) (sin k))
11.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
13.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
46.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
178.0ms
(* (pow t 3.0) (sin k))
466.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
337.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
887.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify122.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09131905
148941506
250011506

prune608.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
3.5b
(/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k))
7.4b
(* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))
16.2b
(* (/ (* 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))))

rewrite210.0ms

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:
2.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
32.0ms
(/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k))
39.0ms
(* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))
119.0ms
(* (/ (* 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))))

series1.7s

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
646.0ms
(/ (* 2.0 (* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))) (tan k))
263.0ms
(* (pow (/ 1 (pow t 3.0)) 1.0) (/ l (sin k)))
669.0ms
(* (/ (* 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))))

simplify63.0ms

Algorithm
egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013973722
150013275

prune916.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 18.8b

localize40.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (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))))
2.4b
(* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k)))
3.5b
(/ (* 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))
16.2b
(* (/ (* 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))))

rewrite1.1s

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:
69.0ms
(* (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))))
74.0ms
(* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k)))
178.0ms
(/ (* 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))
668.0ms
(* (/ (* 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))))

series1.8s

Counts
4 → 12
Calls
4 calls:
302.0ms
(* (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))))
307.0ms
(* (pow (/ (cbrt 1) (pow (cbrt t) 3.0)) 1.0) (/ l (sin k)))
477.0ms
(/ (* 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))
704.0ms
(* (/ (* 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))))

simplify205.0ms

Algorithm
egg-herbie
Counts
831 → 831
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0290719000
1500118352

prune1.8s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 17.6b

regimes832.0ms

Accuracy

0% (2.5b remaining)

Error of 22.6b against oracle of 20.1b and baseline of 22.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03834
13834

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.7s2071×body1280valid
929.0ms1768×body640valid
674.0ms5961×body80valid
308.0ms844×body320valid
105.0ms432×body160valid