Details

Time bar (total: 9.8s)

sample468.0ms

Algorithm
intervals
Results
115.0ms46×body2560valid
62.0ms94×body1280valid
15.0ms57×body640valid
7.0ms37×body320valid
2.0ms15×body160valid
1.0ms7×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.4b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.0b
(- x (sin x))
1.2b
(- x (tan x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×fma-neg
5×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×flip3-- flip--
3×pow1 expm1-log1p-u log1p-expm1-u
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-sub div-exp clear-num div-inv
Counts
3 → 110
Calls
3 calls:
26.0ms
(/ (- x (sin x)) (- x (tan x)))
4.0ms
(- x (sin x))
6.0ms
(- x (tan x))

series175.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ (- x (sin x)) (- x (tan x)))
37.0ms
(- x (sin x))
62.0ms
(- x (tan x))

simplify58.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04721059
11737854
25001854

prune218.0ms

Filtered
119 candidates to 79 candidates (66.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1163119
Fresh000
Picked011
Done000
Total1164120

Merged error: 0b

Counts
120 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma 27/2800 (pow x 4) 1/2)
15.3b
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(fma 27/2800 (pow x 4) 1/2)
1.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series126.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(fma 27/2800 (pow x 4) 1/2)
44.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify148.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune67.0ms

Filtered
26 candidates to 20 candidates (76.9%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New26026
Fresh022
Picked011
Done011
Total26430

Merged error: 0b

Counts
30 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.0b
(- x (sin x))
1.5b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
29.7b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
15×times-frac
9×prod-diff
6×add-exp-log add-cbrt-cube add-log-exp
5×associate-/l* distribute-lft-out-- difference-of-squares
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-prod fma-neg associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg pow1/3 diff-log div-sub div-exp clear-num fma-udef div-inv
Counts
4 → 91
Calls
4 calls:
1.0ms
(cbrt x)
4.0ms
(- x (sin x))
9.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.0s

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt x)
37.0ms
(- x (sin x))
500.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
322.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03421106
11185942
25001904

prune241.0ms

Filtered
103 candidates to 79 candidates (76.7%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1030103
Fresh011
Picked011
Done022
Total1034107

Merged error: 0b

Counts
107 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (- x (sin x))) (sqrt (- x (sin x))))
1.0b
(- x (sin x))
1.0b
(- x (sin x))
1.2b
(- x (tan x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
53×*-un-lft-identity
33×add-cube-cbrt
30×sqrt-prod
27×prod-diff
19×pow1
12×sqrt-div swap-sqr
10×add-log-exp
9×flip3-- fma-neg flip-- distribute-lft-out--
8×sqrt-pow1 pow1/2 associate-*r* associate-*l*
7×difference-of-squares
6×add-exp-log add-cbrt-cube
5×pow-prod-up
4×expm1-log1p-u frac-times log1p-expm1-u unswap-sqr
3×sub-neg diff-log pow-prod-down pow-sqr
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 151
Calls
4 calls:
12.0ms
(* (sqrt (- x (sin x))) (sqrt (- x (sin x))))
4.0ms
(- x (sin x))
4.0ms
(- x (sin x))
4.0ms
(- x (tan x))

series156.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (sqrt (- x (sin x))) (sqrt (- x (sin x))))
30.0ms
(- x (sin x))
31.0ms
(- x (sin x))
55.0ms
(- x (tan x))

simplify64.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04301145
11620827
25001813

prune287.0ms

Filtered
163 candidates to 90 candidates (55.2%)
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1630163
Fresh000
Picked011
Done033
Total1634167

Merged error: 0b

Counts
167 → 4

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.7b

bsearch91.0ms

Steps
ItersRangePoint
10
8.416769919470913e-17
1.2368608357549227
0.02823578267618705
11
-55383.34621353126
-7.66540900750845e-16
-0.02866916276075434

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02510
12510

end0.0ms

sample6.4s

Algorithm
intervals
Results
3.9s1565×body2560valid
1.6s2760×body1280valid
504.0ms1851×body640valid
172.0ms935×body320valid
65.0ms522×body160valid
28.0ms367×body80valid