Details

Time bar (total: 9.5s)

sample540.0ms

Algorithm
intervals
Results
120.0ms57×body2560valid
87.0ms104×body1280valid
16.0ms46×body640valid
8.0ms28×body320valid
1.0ms9×body160valid
1.0ms12×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize11.0ms

Local error

Found 2 expressions with local error:

1.1b
(- x (tan x))
1.1b
(- x (sin x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 28
Calls
2 calls:
5.0ms
(- x (tan x))
8.0ms
(- x (sin x))

series96.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(- x (tan x))
38.0ms
(- x (sin x))

simplify66.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0150157
1342147
2774147
32023147
45001147

prune84.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 31.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin x) (sin x))
1.1b
(- x (tan x))
1.1b
(- (* x x) (* (sin x) (sin x)))
17.1b
(/ (- (* x x) (* (sin x) (sin x))) (+ x (sin x)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
22×add-sqr-sqrt
18×add-cube-cbrt
16×times-frac
11×pow1
8×add-exp-log add-cbrt-cube add-log-exp
7×difference-of-squares
5×distribute-lft-out
4×associate-/r* associate-/l*
3×flip3-- swap-sqr associate-*r* associate-*l* flip--
2×sub-neg diff-log associate-/r/ sqr-sin associate-/l/
1×cbrt-undiv pow2 frac-2neg flip3-+ pow-plus div-sub div-exp pow-prod-down prod-exp clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv sin-mult distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 96
Calls
4 calls:
14.0ms
(* (sin x) (sin x))
5.0ms
(- x (tan x))
8.0ms
(- (* x x) (* (sin x) (sin x)))
25.0ms
(/ (- (* x x) (* (sin x) (sin x))) (+ x (sin x)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (sin x) (sin x))
47.0ms
(- x (tan x))
59.0ms
(- (* x x) (* (sin x) (sin x)))
99.0ms
(/ (- (* x x) (* (sin x) (sin x))) (+ x (sin x)))

simplify60.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0439830
11956748
25001740

prune264.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 31.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b
(- x (tan x))
2.0b
(/ (/ (- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4))) (+ x (sin x))) (- x (tan x)))
9.6b
(- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4)))
29.0b
(/ (- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4))) (+ x (sin x)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
164×*-un-lft-identity
120×add-sqr-sqrt
80×add-cube-cbrt
22×distribute-lft-out
21×associate-/l*
20×distribute-lft-out-- difference-of-squares
16×associate-/r/
11×add-exp-log add-cbrt-cube
9×associate-/r*
8×div-inv add-log-exp
7×flip3-+ flip-+
4×pow1 cbrt-undiv flip3-- div-exp flip--
3×div-sub associate-/l/
2×sub-neg frac-2neg diff-log clear-num
Counts
4 → 193
Calls
4 calls:
5.0ms
(- x (tan x))
38.0ms
(/ (/ (- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4))) (+ x (sin x))) (- x (tan x)))
7.0ms
(- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4)))
28.0ms
(/ (- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4))) (+ x (sin x)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- x (tan x))
139.0ms
(/ (/ (- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4))) (+ x (sin x))) (- x (tan x)))
59.0ms
(- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4)))
99.0ms
(/ (- (* x x) (* (* (cbrt (sin x)) (cbrt (sin x))) (pow (cbrt (sin x)) 4))) (+ x (sin x)))

simplify108.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
08495210
136934977
250024826

prune597.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.1b
(* 9/40 (pow x 2))
18.3b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
9×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×sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- sum-log flip-- associate--r+
Counts
3 → 66
Calls
3 calls:
13.0ms
(* 27/2800 (pow x 4))
11.0ms
(* 9/40 (pow x 2))
17.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series99.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 27/2800 (pow x 4))
23.0ms
(* 9/40 (pow x 2))
40.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0273349
11123318
25001315

prune132.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch65.0ms

Steps
ItersRangePoint
9
1.3330246063773173e-09
3.618674152218468
0.02800287222077787
7
-0.23317146499959118
-0.002309702793432406
-0.027483001552600198

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02911
12911

end0.0ms

sample6.5s

Algorithm
intervals
Results
3.5s1604×body2560valid
1.8s2796×body1280valid
595.0ms1853×body640valid
196.0ms898×body320valid
70.0ms476×body160valid
32.0ms373×body80valid