Details

Time bar (total: 7.9s)

sample85.0ms

Algorithm
intervals
Results
37.0ms103×body1280valid
21.0ms22×body2560valid
10.0ms51×body640valid
4.0ms26×body320valid
2.0ms39×body80valid
1.0ms15×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: 36.2b

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (tan (+ x eps)) (tan x))
3.5b
(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))

series137.0ms

Counts
2 → 6
Calls
2 calls:
88.0ms
(- (tan (+ x eps)) (tan x))
49.0ms
(tan (+ x eps))

simplify76.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0192420
1538319
22593310
35001255

prune115.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.3b

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))
1.8b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite39.0ms

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))
9.0ms
(/ (+ (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))

series750.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(+ (tan x) (tan eps))
204.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms
(* (tan x) (tan eps))
369.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify74.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05592923
120542373
250012349

prune419.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.2b

localize21.0ms

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)
1.8b
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
40×tan-quot
21×add-exp-log add-cbrt-cube
19×frac-times pow-prod-down
13×associate-*r/ associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u associate-*r* associate-*l* pow-sqr pow-prod-up log1p-expm1-u add-log-exp
3×cube-div pow-unpow
2×pow-pow pow-plus pow-exp *-commutative rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod swap-sqr fma-udef unswap-sqr sqr-pow
Counts
4 → 111
Calls
4 calls:
6.0ms
(* (tan x) (tan eps))
15.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
6.0ms
(pow (* (tan x) (tan eps)) 3)
1.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (tan x) (tan eps))
107.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
117.0ms
(pow (* (tan x) (tan eps)) 3)
863.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

simplify110.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06791189
138411058
250011053

prune454.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

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)
0.8b
(- (/ (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)))

rewrite42.0ms

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 (sin x) 3)
3.0ms
(pow (sin x) 3)
3.0ms
(pow (sin x) 3)
20.0ms
(- (/ (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)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sin x) 3)
34.0ms
(pow (sin x) 3)
29.0ms
(pow (sin x) 3)
256.0ms
(- (/ (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 (92.0ms)

IterNodesCost
07418002
131605750
250035716

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes219.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
073152
178152
278152

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.2s3228×body1280valid
547.0ms632×body2560valid
380.0ms1863×body640valid
107.0ms801×body320valid
48.0ms1103×body80valid
34.0ms373×body160valid