Details

Time bar (total: 7.7s)

sample83.0ms

Algorithm
intervals
Results
34.0ms95×body1280valid
21.0ms25×body2560valid
13.0ms64×body640valid
3.0ms21×body320valid
2.0ms43×body80valid
1.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

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: 35.6b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b
(- (tan (+ x eps)) (tan x))
4.6b
(tan (+ x eps))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×tan-quot add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u tan-sum frac-sub add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
7.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series146.0ms

Counts
2 → 6
Calls
2 calls:
91.0ms
(- (tan (+ x eps)) (tan x))
54.0ms
(tan (+ x eps))

simplify74.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0192420
1538319
22593310
35001255

prune109.0ms

Filtered
47 candidates to 33 candidates (70.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New38947
Fresh000
Picked101
Done000
Total39948

Merged error: 13.9b

Counts
48 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b
(* (tan x) (tan eps))
1.5b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
73×add-sqr-sqrt
66×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
9×tan-quot
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1 flip3-- flip--
5×div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-def associate-*r* associate-*l* associate-/r* associate-/l/
2×flip3-+ frac-add 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 distribute-lft-out-- unswap-sqr
Counts
4 → 169
Calls
4 calls:
5.0ms
(+ (tan x) (tan eps))
8.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms
(* (tan x) (tan eps))
14.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series772.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(+ (tan x) (tan eps))
215.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
96.0ms
(* (tan x) (tan eps))
367.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify77.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05592923
120542373
250012349

prune372.0ms

Filtered
181 candidates to 110 candidates (60.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New17110181
Fresh448
Picked101
Done000
Total17614190

Merged error: 13.7b

Counts
190 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.3b
(pow (* (tan x) (tan eps)) 3)
1.5b
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×tan-quot
11×pow1 add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cube-div frac-times pow-unpow associate-*r/ pow-prod-down associate-*l/ prod-exp cbrt-unprod
2×pow-pow pow-exp *-commutative rem-cube-cbrt unswap-sqr
1×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod fma-udef sqr-pow
Counts
4 → 83
Calls
4 calls:
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
6.0ms
(pow (* (tan x) (tan eps)) 3)
1.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (tan x) (tan eps))
94.0ms
(* (tan x) (tan eps))
130.0ms
(pow (* (tan x) (tan eps)) 3)
901.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

simplify72.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0489922
12636827
25002826

prune426.0ms

Filtered
95 candidates to 73 candidates (76.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New91495
Fresh9413
Picked101
Done000
Total1018109

Merged error: 0.1b

Counts
109 → 8

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(pow (cos x) 3)
0.4b
(pow (cos x) 3)
2.2b
(- (/ (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)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
131×times-frac
117×prod-diff
113×*-un-lft-identity
111×add-sqr-sqrt
106×add-cube-cbrt
28×associate-*l/ associate-/r/
25×div-inv
15×flip3-- flip--
9×unpow-prod-down pow-unpow fma-neg cube-prod
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
4×expm1-log1p-u distribute-rgt-out-- log1p-expm1-u
3×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
2×distribute-lft-out-- difference-of-squares
1×sub-neg diff-log frac-sub
Counts
4 → 224
Calls
4 calls:
3.0ms
(pow (cos x) 3)
3.0ms
(pow (cos x) 3)
3.0ms
(pow (cos x) 3)
21.0ms
(- (/ (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)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (cos x) 3)
36.0ms
(pow (cos x) 3)
30.0ms
(pow (cos x) 3)
258.0ms
(- (/ (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)))

simplify143.0ms

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07358188
131845286
250025018

prune1.0s

Filtered
236 candidates to 80 candidates (33.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2360236
Fresh077
Picked011
Done000
Total2368244

Merged error: 0.1b

Counts
244 → 8

regimes135.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
064118
164118

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.3s3306×body1280valid
520.0ms614×body2560valid
379.0ms1831×body640valid
103.0ms779×body320valid
46.0ms1139×body80valid
30.0ms331×body160valid