Details

Time bar (total: 19.8s)

sample146.0ms

Algorithm
intervals
Results
57.0ms67×body1280valid
29.0ms52×body640valid
23.0ms187×body80valid
17.0ms36×body320valid
3.0ms11×body160valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
04813
116113
294413
3500212

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.1b

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.1b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.3b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.1b
(/ (pow t 3.0) (* l l))

rewrite337.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 152
Calls
4 calls:
14.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
33.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
277.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
246.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
315.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
628.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
179.0ms
(/ (pow t 3.0) (* l l))

simplify119.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08171679
147261405
250011405

prune567.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.8b

localize31.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.3b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite533.0ms

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
184×prod-exp
78×add-cbrt-cube
77×div-exp
50×add-sqr-sqrt
49×times-frac
44×associate-*l/ cbrt-unprod
42×*-un-lft-identity
37×add-cube-cbrt
36×associate-*l*
34×frac-times
33×pow-exp
29×pow1
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
12×cbrt-undiv
11×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+ sqr-pow
5×associate-/l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 237
Calls
4 calls:
73.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
19.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
423.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
356.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
236.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
192.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
716.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013643882
150013394

prune1.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
3.1b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.3b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite698.0ms

Algorithm
rewrite-expression-head
Rules
1369×add-exp-log
791×prod-exp
489×div-exp
224×pow-exp
134×pow-to-exp
115×add-cbrt-cube
63×cbrt-unprod
44×associate-*l/
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×frac-times times-frac
30×pow1 add-cube-cbrt
26×unpow-prod-down
25×cbrt-undiv
17×pow-prod-down
16×tan-quot
14×associate-*r/
13×cbrt-prod
11×associate-*r*
8×flip3-+ flip-+
5×unswap-sqr sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 div-inv
Counts
4 → 386
Calls
4 calls:
2.0ms
(pow (cbrt t) 3.0)
103.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
17.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
532.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
648.0ms
(pow (cbrt t) 3.0)
366.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
237.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
748.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
398 → 398
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
018808876
150018023

prune1.2s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 8.4b

localize37.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.4b
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
11.9b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite881.0ms

Algorithm
rewrite-expression-head
Rules
966×add-exp-log
593×prod-exp
294×div-exp
145×pow-exp
103×add-cbrt-cube
87×pow-to-exp
83×times-frac
58×add-sqr-sqrt
53×cbrt-unprod
50×*-un-lft-identity
45×add-cube-cbrt
36×associate-*l*
28×associate-*l/
26×unpow-prod-down
25×associate-*r/
23×cbrt-undiv
19×frac-times associate-/r*
14×tan-quot
13×pow1
11×associate-*r* associate-/l/
10×cbrt-prod sqr-pow
8×flip3-+ flip-+
5×pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×*-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/ associate-/l*
Counts
4 → 351
Calls
4 calls:
67.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
344.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
423.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
356.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
234.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
743.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
844.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify103.0ms

Algorithm
egg-herbie
Counts
363 → 363
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
017688198
150027556

prune1.2s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 6.1b

regimes895.0ms

Accuracy

32.2% (4.9b remaining)

Error of 12.0b against oracle of 7.1b and baseline of 14.4b

bsearch382.0ms

Steps
ItersRangePoint
8
1.6240388381260459e-55
3.4082047793400453e-51
1.673651301516006e-53
9
-1.0221318808867642e-94
-5.3590794823999126e-101
-5.417206106593105e-101

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
085142
185142

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.8s2039×body1280valid
956.0ms1636×body640valid
766.0ms6034×body80valid
351.0ms853×body320valid
117.0ms435×body160valid