Details

Time bar (total: 12.3s)

sample469.0ms

Algorithm
intervals
Results
126.0ms54×body2560valid
55.0ms86×body1280valid
24.0ms67×body640valid
6.0ms28×body320valid
2.0ms14×body160valid
1.0ms7×body80valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
069
1139
2179
3199
done199

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
0.8b
(- x (sin x))
0.8b
(- x (tan x))

rewrite36.0ms

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:
12.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
17.0ms
(- x (tan x))

series174.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ (- x (sin x)) (- x (tan x)))
37.0ms
(- x (sin x))
61.0ms
(- x (tan x))

simplify1.2s

Counts
89 → 89
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01571237
13661200
29591147
326701147
done50001145

prune217.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.1b
(* 9/40 (pow x 2))
16.6b
(- (* 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))
6.0ms
(* 9/40 (pow x 2))
8.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series117.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* 27/2800 (pow x 4))
25.0ms
(* 9/40 (pow x 2))
51.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify1.2s

Counts
75 → 75
Iterations

Useful iterations: 3 (381.0ms)

IterNodesCost
0121788
1279703
2796643
32534637
done5001637

prune150.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (tan x))
0.3b
(- (sqrt x) (sqrt (tan x)))
0.8b
(- x (sin x))
0.8b
(- x (sin x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×*-un-lft-identity
10×add-log-exp
9×sqrt-prod
6×difference-of-squares
5×pow1 add-cube-cbrt
4×add-exp-log add-cbrt-cube distribute-lft-out--
3×sub-neg flip3-- diff-log flip--
1×tan-quot rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 60
Calls
4 calls:
1.0ms
(sqrt (tan x))
6.0ms
(- (sqrt x) (sqrt (tan x)))
3.0ms
(- x (sin x))
3.0ms
(- x (sin x))

series148.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (tan x))
51.0ms
(- (sqrt x) (sqrt (tan x)))
35.0ms
(- x (sin x))
31.0ms
(- x (sin x))

simplify1.5s

Counts
72 → 72
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0104657
1211611
2476571
31099567
42630562
done5000558

prune216.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch92.0ms

Steps
ItersRangePoint
10
3.2824798326487284e-15
0.08347146558812443
0.02869830051678616
9
-5.7596417613087905
-6.7357437175194845e-09
-0.026775790768781334

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02339
12931
done2931

end0.0ms

sample6.6s

Algorithm
intervals
Results
3.5s1574×body2560valid
1.9s2759×body1280valid
675.0ms1927×body640valid
220.0ms930×body320valid
73.0ms457×body160valid
34.0ms353×body80valid