Details

Time bar (total: 10.9s)

analyze1.3s

Algorithm
search

sample248.0ms

Algorithm
intervals
Results
154.0ms58×body2560valid
61.0ms90×body1280valid
14.0ms56×body640valid
5.0ms25×body320valid
2.0ms17×body160valid
1.0ms10×body80valid

simplify386.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.0b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.4b
(- x (tan x))
1.4b
(- x (sin x))

rewrite20.0ms

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:
7.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series37.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(/ (- x (sin x)) (- x (tan x)))
11.0ms
(- x (tan x))
13.0ms
(- x (sin x))

simplify148.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0363718
11148684
24781684
35001684

prune103.0ms

Filtered
63 candidates to 89 candidates (-41.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New85489
Fresh000
Picked101
Done000
Total86490

Merged error: 0.0b

Counts
90 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 27/2800 (pow x 4))
0.1b
(* 9/40 (pow x 2))
14.3b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite18.0ms

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

series15.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(* 27/2800 (pow x 4))
3.0ms
(* 9/40 (pow x 2))
8.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify43.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0273349
11123316
25001313

prune104.0ms

Filtered
46 candidates to 75 candidates (-63.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh033
Picked011
Done000
Total75479

Merged error: 0.0b

Counts
79 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (sin x))
1.4b
(- x (sin x))
1.4b
(- x (sin x))

rewrite15.0ms

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 (tan x))
4.0ms
(- x (sin x))
4.0ms
(- x (sin x))
4.0ms
(- x (sin x))

series23.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(- x (tan x))
4.0ms
(- x (sin x))
4.0ms
(- x (sin x))
5.0ms
(- x (sin x))

simplify68.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0150309
1342288
2774288
32023288
45001288

prune70.0ms

Filtered
49 candidates to 68 candidates (-38.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New68068
Fresh022
Picked011
Done011
Total68472

Merged error: 0.0b

Counts
72 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
1.4b
(- (* x x) (* (tan x) (tan x)))
1.4b
(- x (sin x))
13.3b
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

rewrite23.0ms

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×tan-quot associate-/r* associate-/l*
3×flip3-- swap-sqr associate-*r* associate-*l* flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-times frac-2neg flip3-+ pow-plus div-sub associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 96
Calls
4 calls:
5.0ms
(* (tan x) (tan x))
3.0ms
(- (* x x) (* (tan x) (tan x)))
3.0ms
(- x (sin x))
9.0ms
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

series50.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (tan x) (tan x))
14.0ms
(- (* x x) (* (tan x) (tan x)))
5.0ms
(- x (sin x))
23.0ms
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

simplify60.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0425855
11908783
25001768

prune85.0ms

Filtered
74 candidates to 108 candidates (-45.9%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1080108
Fresh011
Picked011
Done022
Total1084112

Merged error: 0.0b

Counts
112 → 4

regimes82.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch55.0ms

Steps
ItersRangePoint
9
1.3188833207342716e-11
0.04359875009013848
0.030195714331259157
9
-83.37297895051435
-9.040409845291135e-07
-0.028548362329150978

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03326
13326

end0.0ms

analyze1.1s

Algorithm
search

sample6.7s

Algorithm
intervals
Results
4.0s1662×body2560valid
1.7s2812×body1280valid
534.0ms1911×body640valid
150.0ms847×body320valid
56.0ms441×body160valid
31.0ms327×body80valid

Profiling

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