Details

Time bar (total: 8.3s)

sample95.0ms

Algorithm
intervals
Results
39.0ms94×body1280valid
22.0ms25×body2560valid
16.0ms67×body640valid
5.0ms32×body320valid
2.0ms30×body80valid
1.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.3b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (tan (+ x eps)) (tan x))
1.9b
(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))

series191.0ms

Counts
2 → 6
Calls
2 calls:
119.0ms
(- (tan (+ x eps)) (tan x))
72.0ms
(tan (+ x eps))

simplify72.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0192420
1538319
22593310
35001255

prune99.0ms

Filtered
47 candidates to 33 candidates (70.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New39847
Fresh000
Picked101
Done000
Total40848

Merged error: 15.8b

Counts
48 → 8

localize15.0ms

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))))
0.3b
(* (tan x) (tan eps))
2.7b
(- (/ (+ (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))
8.0ms
(/ (+ (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))

series738.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (tan x) (tan eps))
225.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
86.0ms
(* (tan x) (tan eps))
340.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify75.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05592915
120542366
250012345

prune367.0ms

Filtered
181 candidates to 110 candidates (60.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New16912181
Fresh437
Picked101
Done000
Total17415189

Merged error: 15.7b

Counts
189 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (tan x) (tan eps))
0.3b
(* (tan x) (tan eps))
2.7b
(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
41×tan-quot
37×add-sqr-sqrt
33×*-un-lft-identity prod-diff
27×add-cube-cbrt
20×add-exp-log times-frac add-cbrt-cube
19×frac-times pow-prod-down
13×associate-*r/ associate-*l/
11×fma-neg
10×prod-exp cbrt-unprod
9×difference-of-squares
8×associate-/r/
7×associate-*r* associate-*l*
6×add-log-exp
5×flip3-- flip--
4×expm1-log1p-u pow-sqr pow-prod-up log1p-expm1-u div-inv
3×*-commutative
2×pow-plus unswap-sqr
1×pow2 sub-neg diff-log swap-sqr frac-sub distribute-lft-out--
Counts
4 → 158
Calls
4 calls:
11.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
13.0ms
(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))

series1.0s

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
89.0ms
(* (tan x) (tan eps))
88.0ms
(* (tan x) (tan eps))
722.0ms
(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))

simplify94.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06522690
129382162
250012157

prune419.0ms

Filtered
170 candidates to 97 candidates (57.1%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1646170
Fresh21214
Picked101
Done000
Total16718185

Merged error: 15.7b

Counts
185 → 18

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan eps))
0.3b
(* (tan x) (tan eps))
0.3b
(* (tan x) (tan eps))
2.8b
(fma (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- (* 1 1) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (+ 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (- (tan x)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×tan-quot
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times associate-*r/ pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×fma-udef
Counts
4 → 79
Calls
4 calls:
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
1.0ms
(fma (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- (* 1 1) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (+ 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (- (tan x)))

series1.4s

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (tan x) (tan eps))
91.0ms
(* (tan x) (tan eps))
92.0ms
(* (tan x) (tan eps))
1.1s
(fma (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- (* 1 1) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (+ 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (- (tan x)))

simplify67.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04401232
122341074
250021073

prune374.0ms

Filtered
91 candidates to 73 candidates (80.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New88391
Fresh71017
Picked101
Done000
Total9613109

Merged error: 13.5b

Counts
109 → 13

regimes202.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 12.8b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
081167
181167

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.5s3285×body1280valid
575.0ms623×body2560valid
480.0ms1875×body640valid
134.0ms780×body320valid
58.0ms1090×body80valid
39.0ms347×body160valid