Details

Time bar (total: 3.4m)

sample85.0ms

Algorithm
intervals
Results
41.0ms103×body1280valid
16.0ms68×body640valid
14.0ms17×body2560valid
2.0ms18×body320valid
2.0ms39×body80valid
1.0ms11×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.7b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (tan (+ x eps)) (tan x))
2.4b
(tan (+ x eps))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
5×tan-quot
4×tan-sum add-log-exp
3×fma-neg frac-sub
2×pow1 add-exp-log +-commutative expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
7.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series150.0ms

Counts
2 → 6
Calls
2 calls:
98.0ms
(- (tan (+ x eps)) (tan x))
52.0ms
(tan (+ x eps))

simplify73.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0203445
1531344
22464335
35001280

prune95.0ms

Filtered
49 candidates to 33 candidates (32.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New391049
Fresh000
Picked101
Done000
Total401050

Merged error: 16.1b

Counts
50 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan eps) (tan x))
4.7b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
352×*-un-lft-identity
305×add-sqr-sqrt
181×times-frac
126×prod-diff
122×add-cube-cbrt
90×difference-of-squares
48×distribute-lft-out
45×distribute-lft-out-- unswap-sqr
42×fma-neg
29×tan-quot
25×associate-*l*
19×frac-sub
18×associate-/r*
10×associate-/r/
8×add-exp-log add-cbrt-cube associate-/l* add-log-exp
6×pow1 flip3-- flip-- associate-/l/
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×fma-def flip3-+ associate-*r* frac-add flip-+
2×frac-2neg clear-num
1×cbrt-undiv +-commutative frac-times sub-neg diff-log associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp sum-log *-commutative cbrt-unprod
Counts
4 → 313
Calls
4 calls:
13.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
5.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan eps) (tan x))
32.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series778.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
95.0ms
(+ (tan x) (tan eps))
93.0ms
(* (tan eps) (tan x))
370.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify115.0ms

Algorithm
egg-herbie
Counts
325 → 325
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
08576288
132885037
250034966

prune465.0ms

Filtered
325 candidates to 150 candidates (53.8%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New31015325
Fresh819
Picked101
Done000
Total31916335

Merged error: 15.9b

Counts
335 → 16

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan eps) (tan x))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b
(pow (* (tan eps) (tan x)) 3)
4.7b
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x))))) (- (tan x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
46×add-sqr-sqrt
36×tan-quot
32×associate-*l*
30×associate-*r*
26×*-un-lft-identity
22×add-cube-cbrt
21×add-exp-log add-cbrt-cube
19×pow-prod-down
18×frac-times
14×swap-sqr unswap-sqr
12×unpow-prod-down associate-*r/ associate-*l/
10×prod-exp cbrt-unprod
7×*-commutative
4×expm1-log1p-u pow-sqr pow-prod-up log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-pow pow-plus pow-exp rem-cube-cbrt
1×pow2 pow-to-exp unpow3 fma-udef sqr-pow
Counts
4 → 156
Calls
4 calls:
5.0ms
(* (tan eps) (tan x))
16.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
6.0ms
(pow (* (tan eps) (tan x)) 3)
1.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x))))) (- (tan x)))

series1.3s

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (tan eps) (tan x))
116.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
130.0ms
(pow (* (tan eps) (tan x)) 3)
924.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x))))) (- (tan x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
08241585
150011397

prune493.0ms

Filtered
168 candidates to 104 candidates (38.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1644168
Fresh10515
Picked101
Done000
Total1759184

Merged error: 0.1b

Counts
184 → 9

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.3b
(pow (cos x) 3)
0.3b
(pow (cos x) 3)
1.7b
(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

rewrite3.9s

Algorithm
rewrite-expression-head
Rules
40113×add-sqr-sqrt
25140×times-frac
18413×unswap-sqr
13503×*-un-lft-identity
12249×unpow-prod-down
12243×sqr-pow
10512×associate-*l*
10308×difference-of-squares
8463×prod-diff
8217×add-cube-cbrt
2608×associate-/r*
1989×frac-sub
690×associate-/l*
667×div-inv
651×fma-neg
230×frac-2neg clear-num
167×associate-*r*
65×distribute-lft-out--
51×*-commutative
28×associate-*l/ associate-/r/
15×flip3-- flip--
14×distribute-rgt-out--
9×pow-unpow
7×pow1 add-exp-log add-cbrt-cube
6×sub-div add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt
1×sub-neg diff-log
Counts
4 → 11217
Calls
4 calls:
2.0ms
(pow (cos x) 3)
2.0ms
(pow (cos x) 3)
2.0ms
(pow (cos x) 3)
947.0ms
(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

series736.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (cos x) 3)
30.0ms
(pow (cos x) 3)
31.0ms
(pow (cos x) 3)
639.0ms
(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

simplify5.9s

Algorithm
egg-herbie
Counts
11229 → 11229
Iterations

Useful iterations: 0 (183.0ms)

IterNodesCost
017327748747

prune3.2m

Filtered
11229 candidates to 10879 candidates (3.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New11223611229
Fresh538
Picked101
Done000
Total11229911238

Merged error: 0.1b

Counts
11238 → 9

regimes274.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061115
161115

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.3s3312×body1280valid
521.0ms610×body2560valid
377.0ms1852×body640valid
104.0ms753×body320valid
44.0ms1098×body80valid
39.0ms375×body160valid