Details

Time bar (total: 9.5s)

sample481.0ms

Algorithm
intervals
Results
127.0ms60×body2560valid
62.0ms85×body1280valid
25.0ms59×body640valid
6.0ms23×body320valid
4.0ms20×body160valid
1.0ms9×body80valid

simplify21.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (12.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.1b
(- x (sin x))
1.1b
(- x (tan x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt *-un-lft-identity
25×times-frac
15×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
5×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×flip3-- flip--
3×pow1
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-sub div-exp clear-num div-inv
Counts
3 → 80
Calls
3 calls:
11.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
5.0ms
(- x (tan x))

series174.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(/ (- x (sin x)) (- x (tan x)))
31.0ms
(- x (sin x))
68.0ms
(- x (tan x))

simplify154.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0363718
11148685
24795685
35001685

prune200.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-log-exp
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 56
Calls
4 calls:
3.0ms
(- x (sin x))
2.0ms
(- x (tan x))
2.0ms
(- x (tan x))
2.0ms
(- x (tan x))

series185.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(- x (sin x))
53.0ms
(- x (tan x))
48.0ms
(- x (tan x))
53.0ms
(- x (tan x))

simplify67.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0150319
1342299
2774299
32023299
45001299

prune193.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.1b
(* 9/40 (pow x 2))
18.1b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite21.0ms

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:
5.0ms
(* 27/2800 (pow x 4))
5.0ms
(* 9/40 (pow x 2))
8.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series110.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 27/2800 (pow x 4))
29.0ms
(* 9/40 (pow x 2))
44.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0273349
11123318
25001315

prune147.0ms

Pruning

3 alts after pruning (2 fresh and 1 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))
18.1b
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite16.0ms

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
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
5×add-log-exp
4×sqr-pow
3×pow1
2×pow-to-exp pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- diff-log flip--
Counts
3 → 64
Calls
3 calls:
5.0ms
(* 27/2800 (pow x 4))
5.0ms
(* 9/40 (pow x 2))
3.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series172.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(* 27/2800 (pow x 4))
30.0ms
(* 9/40 (pow x 2))
106.0ms
(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify41.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0249310
11003281
25001275

prune143.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.5b

bsearch97.0ms

Steps
ItersRangePoint
8
0.007618006570916684
21.02059315853866
0.028005501728951204
11
-7.192008941699975e+16
-0.00038629318802677867
-0.028952141886034028

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03226
13226

end0.0ms

sample7.1s

Algorithm
intervals
Results
3.8s1621×body2560valid
2.1s2706×body1280valid
753.0ms1926×body640valid
237.0ms901×body320valid
96.0ms510×body160valid
36.0ms336×body80valid