Details

Time bar (total: 9.3s)

sample95.0ms

Algorithm
intervals
Results
50.0ms115×body1280valid
20.0ms24×body2560valid
11.0ms54×body640valid
3.0ms18×body320valid
1.0ms33×body80valid
1.0ms12×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: 37.7b

localize9.0ms

Local error

Found 2 expressions with local error:

1.8b
(- (tan (+ x eps)) (tan x))
3.6b
(tan (+ x eps))

rewrite11.0ms

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))

series134.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(- (tan (+ x eps)) (tan x))
48.0ms
(tan (+ x eps))

simplify73.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0192420
1538319
22593310
35001255

prune122.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.8b

localize12.0ms

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))
3.2b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite37.0ms

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:
4.0ms
(+ (tan x) (tan eps))
8.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms
(* (tan x) (tan eps))
13.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series733.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(+ (tan x) (tan eps))
205.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
92.0ms
(* (tan x) (tan eps))
344.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify69.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05592915
120542366
250012345

prune445.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.6b

localize24.0ms

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)
3.2b
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (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))
5.0ms
(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)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (tan x) (tan eps))
91.0ms
(* (tan x) (tan eps))
124.0ms
(pow (* (tan x) (tan eps)) 3)
866.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

simplify73.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0483922
12591827
25002826

prune487.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

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)
1.2b
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (* (pow (cos x) 2) (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)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
60×add-sqr-sqrt
55×add-cube-cbrt
52×prod-diff
37×times-frac
18×frac-add
15×distribute-lft-out
13×add-log-exp
11×frac-sub
9×unpow-prod-down pow-unpow cube-prod
7×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u flip3-+ fma-neg flip-+ log1p-expm1-u div-inv
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-- associate-*l/ associate--l+ flip--
Counts
4 → 163
Calls
4 calls:
3.0ms
(pow (sin x) 3)
3.0ms
(pow (sin x) 3)
3.0ms
(pow (sin x) 3)
43.0ms
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (* (pow (cos x) 2) (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:
30.0ms
(pow (sin x) 3)
34.0ms
(pow (sin x) 3)
30.0ms
(pow (sin x) 3)
1.3s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (* (pow (cos x) 2) (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)))

simplify129.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0134713932
1500212199

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes171.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
062134
162134

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s3312×body1280valid
583.0ms676×body2560valid
379.0ms1768×body640valid
106.0ms761×body320valid
50.0ms1117×body80valid
37.0ms366×body160valid