Details

Time bar (total: 9.8s)

sample234.0ms

Algorithm
intervals
Results
170.0ms118×body2560valid
36.0ms68×body1280valid
10.0ms40×body640valid
3.0ms256×pre80true
3.0ms17×body320valid
2.0ms13×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
1114
2114

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (tan x))
2.6b
(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×*-un-lft-identity
19×times-frac
12×add-cube-cbrt
5×distribute-lft-out--
4×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
3×associate-/r* div-inv associate-/l*
2×pow1
1×tan-quot cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num associate-/r/ frac-sub flip--
Counts
2 → 50
Calls
2 calls:
2.0ms
(/ 1.0 (tan x))
18.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

series140.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ 1.0 (tan x))
104.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify53.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0232342
1610327
21894327
35001326

prune117.0ms

Filtered
56 candidates to 46 candidates (82.1%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.0b
(* 0.0021164021164021165 (pow x 5))
0.1b
(* 0.022222222222222223 (pow x 3))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1 sum-log
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult associate-+r+ flip3-+ unpow3 flip-+
Counts
3 → 69
Calls
3 calls:
9.0ms
(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
5.0ms
(* 0.0021164021164021165 (pow x 5))
7.0ms
(* 0.022222222222222223 (pow x 3))

series147.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
50.0ms
(* 0.0021164021164021165 (pow x 5))
35.0ms
(* 0.022222222222222223 (pow x 3))

simplify43.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0301381
11298348
25002348

prune161.0ms

Filtered
78 candidates to 49 candidates (62.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
0.0b
(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
0.0b
(* 0.0021164021164021165 (pow x 5))
0.1b
(* 0.022222222222222223 (pow x 3))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sum-log sqr-pow
2×+-commutative pow-to-exp flip3-+ pow-exp *-commutative cbrt-unprod flip-+
1×cube-mult associate-+l+ unpow3
Counts
4 → 80
Calls
4 calls:
3.0ms
(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
19.0ms
(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
6.0ms
(* 0.0021164021164021165 (pow x 5))
7.0ms
(* 0.022222222222222223 (pow x 3))

series280.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
61.0ms
(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
52.0ms
(* 0.0021164021164021165 (pow x 5))
36.0ms
(* 0.022222222222222223 (pow x 3))

simplify50.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0349485
11525454
25002454

prune203.0ms

Filtered
92 candidates to 58 candidates (63.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.6b
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
68.0ms
(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
8.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
8.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
11.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series1.1s

Counts
4 → 12
Calls
4 calls:
316.0ms
(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
270.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
274.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
269.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify66.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04962207
119322080
250011862

prune349.0ms

Filtered
99 candidates to 75 candidates (75.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

regimes74.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0187
1187

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.4s3219×body2560valid
1.4s2489×body1280valid
343.0ms1307×body640valid
105.0ms609×body320valid
95.0ms8000×pre80true
41.0ms328×body160valid
3.0ms48×body80valid