Details

Time bar (total: 5.2s)

analyze790.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.2%0.1%6
21.9%78%0.1%7
23.4%76.5%0.1%8
24.2%75.7%0.1%9
24.6%75.3%0.1%10
24.8%75.1%0.1%11
24.9%75%0.1%12
24.9%75%0.1%13
25%75%0.1%14

sample83.0ms

Algorithm
intervals
Results
40.0ms100×body1280valid
13.0ms61×body640valid
13.0ms15×body2560valid
5.0ms32×body320valid
2.0ms16×body160valid
1.0ms32×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.9b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (tan (+ x eps)) (tan x))
2.8b
(tan (+ x eps))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×tan-quot add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt tan-sum frac-sub add-cbrt-cube
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
6.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series41.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(- (tan (+ x eps)) (tan x))
17.0ms
(tan (+ x eps))

simplify50.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
04924332
14924332

prune70.0ms

Filtered
25 candidates to 30 candidates (-20.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New21930
Fresh000
Picked101
Done000
Total22931

Merged error: 13.3b

Counts
31 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
2.9b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
9×tan-quot
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1
5×distribute-lft-out
4×associate-/l*
3×associate-*r* associate-*l* associate-/r* associate-/l/
2×flip3-- flip3-+ frac-add associate-/r/ flip-- flip-+ difference-of-squares
1×cbrt-undiv +-commutative frac-times sub-neg frac-2neg diff-log associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num sum-log *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 85
Calls
4 calls:
8.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
12.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series201.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms
(+ (tan x) (tan eps))
23.0ms
(* (tan x) (tan eps))
101.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify53.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
051091560

prune177.0ms

Filtered
74 candidates to 97 candidates (-31.1%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New831497
Fresh628
Picked101
Done000
Total9016106

Merged error: 13.2b

Counts
106 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(exp (tan x))
0.5b
(pow (exp (tan x)) (tan eps))
2.7b
(log (pow (exp (tan x)) (tan eps)))
2.9b
(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt
7×log-prod add-log-exp
6×unpow-prod-down exp-prod
5×pow1 add-exp-log
4×pow-pow add-cbrt-cube
3×pow-unpow rem-log-exp
2×pow-to-exp pow-exp difference-of-squares sqr-pow
1×tan-quot sub-neg flip3-- times-frac diff-log log-pow frac-sub flip-- rem-exp-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
2.0ms
(exp (tan x))
4.0ms
(pow (exp (tan x)) (tan eps))
3.0ms
(log (pow (exp (tan x)) (tan eps)))
16.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

series211.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(exp (tan x))
31.0ms
(pow (exp (tan x)) (tan eps))
38.0ms
(log (pow (exp (tan x)) (tan eps)))
129.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

simplify49.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04934920
14934920

prune123.0ms

Filtered
52 candidates to 76 candidates (-46.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New74276
Fresh6915
Picked101
Done000
Total811192

Merged error: 11.4b

Counts
92 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow E (tan x))
0.5b
(pow (pow E (tan x)) (tan eps))
2.7b
(log (pow (pow E (tan x)) (tan eps)))
2.9b
(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (pow E (tan x)) (tan eps))))) (tan x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
23×unpow-prod-down
17×add-sqr-sqrt
14×*-un-lft-identity pow-exp
12×add-cube-cbrt
11×log-prod
10×add-exp-log
6×pow-unpow rem-log-exp add-log-exp
5×pow1 pow-to-exp sqr-pow
4×add-cbrt-cube
3×e-exp-1
2×pow-pow difference-of-squares
1×tan-quot sub-neg flip3-- times-frac diff-log log-pow frac-sub flip-- distribute-lft-out--
Counts
4 → 82
Calls
4 calls:
2.0ms
(pow E (tan x))
4.0ms
(pow (pow E (tan x)) (tan eps))
4.0ms
(log (pow (pow E (tan x)) (tan eps)))
17.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (pow E (tan x)) (tan eps))))) (tan x))

series229.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(pow E (tan x))
34.0ms
(pow (pow E (tan x)) (tan eps))
42.0ms
(log (pow (pow E (tan x)) (tan eps)))
133.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (pow E (tan x)) (tan eps))))) (tan x))

simplify61.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
050211073

prune83.0ms

Filtered
56 candidates to 94 candidates (-67.9%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh01010
Picked011
Done000
Total9411105

Merged error: 11.4b

Counts
105 → 11

regimes166.0ms

Accuracy

95.1% (0.4b remaining)

Error of 13.2b against oracle of 12.7b and baseline of 21.7b

bsearch66.0ms

Steps
ItersRangePoint
8
1.2880116290406164e-43
8.05512871121911e-39
7.872211594490747e-39
9
-7.104489460126275e-08
-5.7598704753563365e-15
-5.841647685826717e-15

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05138
15138

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s3300×body1280valid
560.0ms656×body2560valid
398.0ms1840×body640valid
111.0ms757×body320valid
52.0ms1115×body80valid
32.0ms332×body160valid

Profiling

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