Details

Time bar (total: 17.0s)

sample136.0ms

Algorithm
intervals
Results
53.0ms66×body1280valid
29.0ms51×body640valid
20.0ms181×body80valid
10.0ms28×body320valid
4.0ms17×body160valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.2b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (pow t 3.0) (sin k))
2.7b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
4.8b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
27.0b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite116.0ms

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:
15.0ms
(* (pow t 3.0) (sin k))
21.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
10.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
62.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (pow t 3.0) (sin k))
336.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
75.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
881.0ms
(* (/ (/ 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 (24.0ms)

IterNodesCost
010192396
150011978

prune774.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.2b

localize21.0ms

Local error

Found 4 expressions with local error:

1.8b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
2.4b
(* (pow t 3.0) (sin k))
6.7b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
18.9b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite172.0ms

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))
15.0ms
(* (pow t 3.0) (sin k))
32.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
93.0ms
(* (/ (* (/ 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:
463.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
181.0ms
(* (pow t 3.0) (sin k))
368.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
916.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify114.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09131905
148941506
250011506

prune612.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.6b

localize27.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
1.8b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
6.7b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
18.9b
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite447.0ms

Algorithm
rewrite-expression-head
Rules
436×add-exp-log
240×prod-exp
146×div-exp
100×add-cbrt-cube
48×pow-exp
40×cbrt-unprod
34×cbrt-undiv
33×add-sqr-sqrt
32×pow-to-exp
28×times-frac
26×add-cube-cbrt *-un-lft-identity
16×associate-*r*
15×associate-*l*
8×pow1
6×associate-/r*
5×div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*l/ unswap-sqr
2×tan-quot frac-2neg pow-prod-down clear-num associate-/r/ *-commutative
1×frac-times associate-*r/ associate-/l/
Counts
4 → 208
Calls
4 calls:
5.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
71.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
99.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
259.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.2s

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
713.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
402.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
971.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify54.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011653923
150013194

prune747.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.9b

localize29.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
1.8b
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
2.0b
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
18.9b
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite528.0ms

Algorithm
rewrite-expression-head
Rules
1780×add-exp-log
960×prod-exp
718×div-exp
196×pow-exp add-cbrt-cube
124×pow-to-exp
96×rec-exp 1-exp
84×cbrt-unprod
70×cbrt-undiv
40×times-frac
37×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
27×associate-*l*
14×associate-*r*
11×pow1
7×associate-*l/
6×associate-/r*
5×div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×frac-times unpow-prod-down associate-*r/ associate-/l/ sqr-pow
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative unswap-sqr
Counts
4 → 478
Calls
4 calls:
5.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
85.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
91.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
299.0ms
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt 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:
90.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
518.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
395.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
939.0ms
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify104.0ms

Algorithm
egg-herbie
Counts
490 → 490
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
019609108
150017782

prune805.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 18.3b

regimes545.0ms

Accuracy

-0.7% (3.1b remaining)

Error of 22.0b against oracle of 18.9b and baseline of 22.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05158
15158

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2087×body1280valid
861.0ms1632×body640valid
658.0ms5864×body80valid
347.0ms899×body320valid
113.0ms443×body160valid