Details

Time bar (total: 8.7s)

sample380.0ms

Algorithm
intervals
Results
205.0ms66×body640valid
101.0ms43×body2560valid
49.0ms96×body1280valid
6.0ms29×body320valid
3.0ms11×body160valid
1.0ms11×body80valid

simplify444.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0199
1199

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.0b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
0.6b
(- x (sin x))
0.9b
(- x (tan x))

rewrite32.0ms

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:
19.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
6.0ms
(- x (tan x))

series39.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(/ (- x (sin x)) (- x (tan x)))
5.0ms
(- x (sin x))
21.0ms
(- x (tan x))

simplify48.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
051961147

prune94.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.0b
(/ (- x (sin x)) (- x (tan x)))
0.6b
(- x (sin x))
0.9b
(- x (tan x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt *-un-lft-identity
50×times-frac
32×log-pow
31×exp-prod
28×add-cube-cbrt
24×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-/r* flip-- associate-/l*
4×associate-/r/
3×log-prod
2×sub-neg diff-log div-sub div-inv associate-/l/
1×cbrt-undiv log-div frac-2neg exp-diff div-exp rem-log-exp clear-num
Counts
4 → 124
Calls
4 calls:
10.0ms
(log (exp (/ (- x (sin x)) (- x (tan x)))))
8.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (sin x))
3.0ms
(- x (tan x))

series44.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(log (exp (/ (- x (sin x)) (- x (tan x)))))
13.0ms
(/ (- x (sin x)) (- x (tan x)))
5.0ms
(- x (sin x))
10.0ms
(- x (tan x))

simplify36.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
049491713
149491713

prune131.0ms

Filtered
96 candidates to 136 candidates (-41.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1351136
Fresh033
Picked011
Done000
Total1355140

Merged error: 0.0b

Counts
140 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- x (tan x)))
0.1b
(* (- x (sin x)) (/ 1 (- x (tan x))))
0.6b
(- x (sin x))
0.9b
(- x (tan x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
45×*-un-lft-identity
32×times-frac
24×add-cube-cbrt
21×associate-*r*
17×add-exp-log
11×add-cbrt-cube
10×distribute-lft-out-- difference-of-squares
8×add-log-exp
7×pow1
6×flip3-- flip--
5×associate-*l* associate-/r*
4×div-exp prod-exp associate-/r/
3×associate-/l* unswap-sqr
2×cbrt-undiv frac-times sub-neg rec-exp diff-log 1-exp associate-*l/ cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 119
Calls
4 calls:
5.0ms
(/ 1 (- x (tan x)))
13.0ms
(* (- x (sin x)) (/ 1 (- x (tan x))))
3.0ms
(- x (sin x))
3.0ms
(- x (tan x))

series40.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ 1 (- x (tan x)))
13.0ms
(* (- x (sin x)) (/ 1 (- x (tan x))))
7.0ms
(- x (sin x))
10.0ms
(- x (tan x))

simplify76.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049341375
149341375

prune106.0ms

Filtered
84 candidates to 131 candidates (-56.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1310131
Fresh033
Picked011
Done011
Total1315136

Merged error: 0.0b

Counts
136 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow x 4) -27/2800)
0.1b
(* x (* x 9/40))
0.2b
(* x 9/40)
18.1b
(+ (* x (* x 9/40)) (+ (* (pow x 4) -27/2800) -1/2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×add-exp-log
13×associate-*l* add-cbrt-cube
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×add-log-exp
7×associate-*r* prod-exp
5×cbrt-unprod
4×unpow-prod-down pow-prod-down unswap-sqr
3×sum-log *-commutative
2×sqr-pow
1×+-commutative pow-to-exp associate-+r+ flip3-+ pow-exp flip-+
Counts
4 → 74
Calls
4 calls:
5.0ms
(* (pow x 4) -27/2800)
4.0ms
(* x (* x 9/40))
3.0ms
(* x 9/40)
8.0ms
(+ (* x (* x 9/40)) (+ (* (pow x 4) -27/2800) -1/2))

series14.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (pow x 4) -27/2800)
3.0ms
(* x (* x 9/40))
2.0ms
(* x 9/40)
6.0ms
(+ (* x (* x 9/40)) (+ (* (pow x 4) -27/2800) -1/2))

simplify55.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
04967650
14967650

prune92.0ms

Filtered
52 candidates to 86 candidates (-65.4%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New85186
Fresh112
Picked011
Done022
Total86591

Merged error: 0.0b

Counts
91 → 5

regimes89.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch41.0ms

Steps
ItersRangePoint
10
0.009091900342010817
66730311810763.45
0.02710029241079174
9
-60.40944958396893
-2.7804654585538832e-05
-0.029403870047242545

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03233
13233

end0.0ms

sample6.8s

Algorithm
intervals
Results
4.2s1629×body2560valid
1.7s2807×body1280valid
489.0ms1804×body640valid
173.0ms937×body320valid
65.0ms463×body160valid
29.0ms360×body80valid

Profiling

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