Details

Time bar (total: 14.0s)

sample152.0ms

Algorithm
intervals
Results
77.0ms103×body1280valid
28.0ms17×body2560valid
23.0ms57×body640valid
10.0ms37×body320valid
3.0ms32×body80valid
2.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize9.0ms

Local error

Found 2 expressions with local error:

1.8b
(- (tan (+ x eps)) (tan x))
3.3b
(tan (+ x eps))

rewrite12.0ms

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:
8.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series151.0ms

Counts
2 → 6
Calls
2 calls:
93.0ms
(- (tan (+ x eps)) (tan x))
58.0ms
(tan (+ x eps))

simplify79.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (24.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune87.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×tan-quot
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l*
2×sub-neg flip3-- diff-log flip-- difference-of-squares
1×+-commutative frac-times flip3-+ times-frac associate-*r/ pow-prod-down associate-*l/ frac-add prod-exp sum-log *-commutative frac-sub cbrt-unprod flip-+ distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
4 → 62
Calls
4 calls:
2.0ms
(- 1 (* (tan x) (tan eps)))
3.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
40.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series661.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- 1 (* (tan x) (tan eps)))
96.0ms
(+ (tan x) (tan eps))
94.0ms
(* (tan x) (tan eps))
362.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify131.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0343662
11170624
24756614
35001614

prune231.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.2b

localize22.0ms

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)
3.4b
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1))) (tan x))

rewrite321.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
13×tan-quot
11×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
9×add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
3×cube-div frac-times pow-unpow times-frac associate-*r/ pow-prod-down associate-*l/ prod-exp cbrt-unprod difference-of-squares
2×pow-pow pow-exp *-commutative rem-cube-cbrt unswap-sqr
1×cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- diff-log unpow3 cube-prod frac-sub flip-- distribute-lft-out-- sqr-pow
Counts
4 → 84
Calls
4 calls:
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
4.0ms
(pow (* (tan x) (tan eps)) 3)
305.0ms
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1))) (tan x))

series1.9s

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (tan x) (tan eps))
94.0ms
(* (tan x) (tan eps))
130.0ms
(pow (* (tan x) (tan eps)) 3)
1.5s
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (pow (* (tan x) (tan eps)) 3)) (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1))) (tan x))

simplify79.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05401247
127471149
250011149

prune357.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos eps) 3)
0.4b
(pow (cos eps) 3)
0.4b
(pow (cos eps) 3)
1.8b
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (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)))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity frac-add
13×add-cube-cbrt add-log-exp
11×frac-sub
9×unpow-prod-down pow-unpow cube-prod
7×pow1 add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×cube-mult frac-times pow-to-exp pow-pow diff-log unpow3 associate-*r/ pow-exp sum-log rem-cube-cbrt sqr-pow
2×distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- times-frac associate-*l/ associate--l+ flip-- distribute-lft-out
Counts
4 → 99
Calls
4 calls:
1.0ms
(pow (cos eps) 3)
1.0ms
(pow (cos eps) 3)
2.0ms
(pow (cos eps) 3)
2.0s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (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)))

series1.4s

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (cos eps) 3)
29.0ms
(pow (cos eps) 3)
29.0ms
(pow (cos eps) 3)
1.3s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (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)))

simplify77.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010105750
150025532

prune882.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

regimes317.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061113
163113
263113

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.5s3319×body1280valid
1.1s623×body2560valid
979.0ms1857×body640valid
219.0ms775×body320valid
89.0ms1072×body80valid
64.0ms354×body160valid