Details

Time bar (total: 10.3s)

sample162.0ms

Algorithm
intervals
Results
80.0ms108×body1280valid
42.0ms25×body2560valid
20.0ms54×body640valid
6.0ms21×body320valid
3.0ms36×body80valid
2.0ms12×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b
(- (tan (+ x eps)) (tan x))
2.2b
(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 → 25
Calls
2 calls:
7.0ms
(- (tan (+ x eps)) (tan x))
3.0ms
(tan (+ x eps))

series140.0ms

Counts
2 → 6
Calls
2 calls:
90.0ms
(- (tan (+ x eps)) (tan x))
50.0ms
(tan (+ x eps))

simplify77.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune90.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(- 1 (* (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))
3.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
7×tan-quot
6×pow1
4×distribute-lft-out associate-/l*
3×flip3-- associate-*r* associate-*l* associate-/r* flip-- associate-/l/
2×sub-neg diff-log associate-/r/ difference-of-squares
1×cbrt-undiv frac-times frac-2neg flip3-+ associate-*r/ div-exp pow-prod-down associate-*l/ frac-add prod-exp clear-num *-commutative frac-sub cbrt-unprod flip-+ div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 85
Calls
4 calls:
11.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
2.0ms
(- 1 (* (tan x) (tan eps)))
5.0ms
(* (tan x) (tan eps))
43.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series793.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
111.0ms
(- 1 (* (tan x) (tan eps)))
96.0ms
(* (tan x) (tan eps))
369.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify50.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04011066
115321014
250011004

prune287.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
0.2b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(* (sin x) (sin eps))
3.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
11×*-un-lft-identity
8×add-log-exp
6×pow1 add-cube-cbrt
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp difference-of-squares
3×associate-*r* associate-*l*
2×sub-neg flip3-- times-frac diff-log flip-- sin-mult distribute-lft-out--
1×tan-quot frac-2neg pow-prod-down clear-num associate-/r* associate-/r/ cos-mult *-commutative frac-sub div-inv associate-/l/ associate-/l* unswap-sqr
Counts
4 → 73
Calls
4 calls:
7.0ms
(- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
6.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
4.0ms
(* (sin x) (sin eps))
101.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

series655.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
103.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
46.0ms
(* (sin x) (sin eps))
381.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

simplify57.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04251036
11955913
25001913

prune514.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (sin eps))
0.2b
(* (sin x) (sin eps))
0.2b
(* (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
3.4b
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (+ 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (tan x))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
138×add-exp-log add-cbrt-cube
67×prod-exp cbrt-unprod
40×cbrt-undiv div-exp
27×add-sqr-sqrt
15×pow1
14×*-un-lft-identity
12×add-cube-cbrt associate-*r* associate-*l*
7×times-frac
6×swap-sqr add-log-exp
4×associate-/r/ cos-mult div-inv
3×pow-prod-down *-commutative difference-of-squares unswap-sqr
2×sin-mult
1×tan-quot pow2 frac-times sub-neg flip3-- pow-plus diff-log associate-*r/ associate-*l/ pow-sqr pow-prod-up frac-sub flip-- distribute-lft-out--
Counts
4 → 140
Calls
4 calls:
4.0ms
(* (sin x) (sin eps))
4.0ms
(* (sin x) (sin eps))
28.0ms
(* (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
147.0ms
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (+ 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (tan x))

series1.3s

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin x) (sin eps))
53.0ms
(* (sin x) (sin eps))
130.0ms
(* (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
1.0s
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (+ 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (tan x))

simplify122.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07193058
145512129
250022104

prune423.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.3b

regimes194.0ms

Accuracy

86.9% (1.0b remaining)

Error of 15.2b against oracle of 14.2b and baseline of 21.7b

bsearch148.0ms

Steps
ItersRangePoint
8
1.412343169719264e-20
6.157903029658734e-17
5.66748466896462e-20
7
-5.424898332662606e-53
-2.572039402824119e-55
-1.803646814354997e-54

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04322
14322

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.5s3321×body1280valid
1.0s618×body2560valid
796.0ms1844×body640valid
187.0ms707×body320valid
95.0ms401×body160valid
92.0ms1109×body80valid