Details

Time bar (total: 13.2s)

sample170.0ms

Algorithm
intervals
Results
89.0ms110×body1280valid
32.0ms71×body640valid
29.0ms14×body2560valid
6.0ms23×body320valid
3.0ms31×body80valid
1.0ms7×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: 37.6b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b
(- (tan (+ x eps)) (tan x))
3.7b
(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:
8.0ms
(- (tan (+ x eps)) (tan x))
3.0ms
(tan (+ x eps))

series143.0ms

Counts
2 → 6
Calls
2 calls:
87.0ms
(- (tan (+ x eps)) (tan x))
56.0ms
(tan (+ x eps))

simplify77.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (23.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune82.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.3b

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))
4.0b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite63.0ms

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 → 86
Calls
4 calls:
3.0ms
(+ (tan x) (tan eps))
11.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms
(* (tan x) (tan eps))
41.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series726.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(+ (tan x) (tan eps))
204.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
87.0ms
(* (tan x) (tan eps))
337.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify46.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03971050
114321005
25001995

prune291.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(pow (* (tan x) (tan eps)) 3)
4.0b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
45×tan-quot
21×add-exp-log frac-times add-cbrt-cube
19×pow-prod-down
15×associate-*r/
14×associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×frac-sub
4×associate-*r* associate-*l* pow-sqr pow-prod-up
3×cube-div pow-unpow
2×pow-pow flip3-+ pow-plus pow-exp associate--l+ *-commutative flip-+ rem-cube-cbrt
1×pow2 distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- distribute-lft-in diff-log unpow3 cube-prod swap-sqr flip-- unswap-sqr sqr-pow
Counts
4 → 114
Calls
4 calls:
5.0ms
(* (tan x) (tan eps))
21.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
4.0ms
(pow (* (tan x) (tan eps)) 3)
37.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series1.8s

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (tan x) (tan eps))
110.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
124.0ms
(pow (* (tan x) (tan eps)) 3)
1.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify126.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
08471739
146891494
250011492

prune419.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin x) 3)
0.4b
(pow (sin x) 3)
0.4b
(pow (sin x) 3)
2.6b
(- (+ (+ (/ (* (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)))

rewrite1.9s

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:
2.0ms
(pow (sin x) 3)
2.0ms
(pow (sin x) 3)
2.0ms
(pow (sin x) 3)
1.9s
(- (+ (+ (/ (* (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)))

series1.3s

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (sin x) 3)
34.0ms
(pow (sin x) 3)
30.0ms
(pow (sin x) 3)
1.2s
(- (+ (+ (/ (* (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)))

simplify74.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010145759
150015543

prune852.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

regimes197.0ms

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
063114
163114

end0.0ms

sample4.7s

Algorithm
intervals
Results
2.3s3290×body1280valid
1.1s658×body2560valid
743.0ms1818×body640valid
204.0ms784×body320valid
97.0ms1119×body80valid
57.0ms331×body160valid