Details

Time bar (total: 9.3s)

sample416.0ms

Algorithm
intervals
Results
84.0ms45×body2560valid
45.0ms88×body1280valid
14.0ms59×body640valid
7.0ms31×body320valid
2.0ms18×body160valid
1.0ms15×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 31.4b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.5b
(- x (tan x))
1.5b
(- x (sin x))

rewrite38.0ms

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:
10.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series182.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(/ (- x (sin x)) (- x (tan x)))
60.0ms
(- x (tan x))
42.0ms
(- x (sin x))

simplify149.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0363718
11148685
24795685
35001685

prune208.0ms

Filtered
89 candidates to 63 candidates (70.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New85489
Fresh000
Picked101
Done000
Total86490

Merged error: 0.0b

Counts
90 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.0b
(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.5b
(- x (tan x))
1.5b
(- x (sin x))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
147×*-un-lft-identity
146×add-sqr-sqrt
100×times-frac
68×cbrt-prod
62×unpow-prod-down cube-prod
54×add-cube-cbrt
46×distribute-lft-out-- difference-of-squares
30×cube-div
15×cbrt-div
10×associate-/r* associate-/l*
8×flip3-- associate-/r/ flip-- add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1
4×pow-unpow div-inv associate-/l/
2×cube-mult sub-neg frac-2neg diff-log unpow3 pow-exp clear-num rem-cbrt-cube rem-cube-cbrt sqr-pow
1×cbrt-undiv pow-to-exp pow-pow pow1/3 div-exp
Counts
4 → 217
Calls
4 calls:
13.0ms
(pow (/ (- x (sin x)) (- x (tan x))) 3)
15.0ms
(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
3.0ms
(- x (tan x))
4.0ms
(- x (sin x))

series259.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(pow (/ (- x (sin x)) (- x (tan x))) 3)
79.0ms
(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
50.0ms
(- x (tan x))
36.0ms
(- x (sin x))

simplify113.0ms

Algorithm
egg-herbie
Counts
229 → 229
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09232456
144112319
250012313

prune370.0ms

Filtered
229 candidates to 106 candidates (46.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2290229
Fresh033
Picked011
Done000
Total2294233

Merged error: 0.0b

Counts
233 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

1.5b
(- x (tan x))
1.5b
(- x (tan x))
1.5b
(- x (sin x))
1.5b
(- x (sin x))

rewrite17.0ms

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

series176.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- x (tan x))
51.0ms
(- x (tan x))
37.0ms
(- x (sin x))
33.0ms
(- x (sin x))

simplify67.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0150314
1342294
2774294
32023294
45001294

prune189.0ms

Filtered
68 candidates to 50 candidates (73.5%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New68068
Fresh022
Picked011
Done011
Total68472

Merged error: 0.0b

Counts
72 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b
(* 27/2800 (pow x 4))
0.4b
(* 9/40 (pow x 2))
13.1b
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
25×*-un-lft-identity
15×associate-*r*
13×add-exp-log
11×associate-*l* unswap-sqr
9×add-cube-cbrt unpow-prod-down
8×add-log-exp
7×pow1 add-cbrt-cube
6×prod-exp distribute-lft-out--
5×difference-of-squares sqr-pow
4×distribute-lft-out
3×unpow2
2×pow-to-exp diff-log pow-prod-down pow-exp *-commutative cbrt-unprod associate--r+
1×+-commutative sub-neg flip3-- sum-log flip--
Counts
3 → 80
Calls
3 calls:
6.0ms
(* 27/2800 (pow x 4))
7.0ms
(* 9/40 (pow x 2))
24.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series114.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* 27/2800 (pow x 4))
24.0ms
(* 9/40 (pow x 2))
49.0ms
(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0297472
11153437
25001434

prune153.0ms

Filtered
89 candidates to 50 candidates (56.2%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New89089
Fresh011
Picked011
Done022
Total89493

Merged error: 0.0b

Counts
93 → 4

regimes72.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch79.0ms

Steps
ItersRangePoint
8
2.0262054515877825e-05
0.3235305135594418
0.020919416033764127
10
-85019.06990604498
-4.503960361653909e-11
-1.5618953286310733

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03126
13126

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.1s1655×body2560valid
1.5s2692×body1280valid
468.0ms1879×body640valid
151.0ms906×body320valid
63.0ms505×body160valid
26.0ms363×body80valid