Details

Time bar (total: 3.9s)

sample91.0ms

Algorithm
intervals
Results
40.0ms103×body1280valid
25.0ms29×body2560valid
10.0ms48×body640valid
5.0ms36×body320valid
1.0ms28×body80valid
1.0ms12×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: 41.0b

Counts
2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

1.4b
(- (tan (+ x eps)) (tan x))
4.0b
(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:
6.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series139.0ms

Counts
2 → 6
Calls
2 calls:
90.0ms
(- (tan (+ x eps)) (tan x))
49.0ms
(tan (+ x eps))

simplify78.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (23.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune85.0ms

Filtered
31 candidates to 25 candidates (80.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New24731
Fresh000
Picked101
Done000
Total25732

Merged error: 16.7b

Counts
32 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite32.0ms

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:
8.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
12.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series762.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
96.0ms
(+ (tan x) (tan eps))
94.0ms
(* (tan x) (tan eps))
357.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03971050
114321005
25001994

prune409.0ms

Filtered
98 candidates to 74 candidates (75.5%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New861298
Fresh336
Picked101
Done000
Total9015105

Merged error: 16.5b

Counts
105 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.1b
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.2b
(* (tan x) (tan eps))
2.6b
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×tan-quot
19×*-un-lft-identity
18×associate-*r*
15×add-exp-log
14×add-cube-cbrt
11×times-frac add-cbrt-cube
8×pow1 frac-sub add-log-exp
7×frac-times associate-*l* associate-*l/
5×flip3-+ frac-add prod-exp flip-+
4×unswap-sqr
3×associate-*r/ cbrt-unprod
2×flip3-- div-exp pow-prod-down associate-/r/ un-div-inv *-commutative flip-- distribute-lft-out
1×cbrt-undiv +-commutative sub-neg rec-exp diff-log 1-exp sum-log div-inv
Counts
4 → 99
Calls
4 calls:
4.0ms
(+ (tan x) (tan eps))
13.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
5.0ms
(* (tan x) (tan eps))
12.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series737.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (tan x) (tan eps))
204.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
88.0ms
(* (tan x) (tan eps))
356.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify67.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05611286
125471185
250011184

prune291.0ms

Filtered
111 candidates to 84 candidates (75.7%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1047111
Fresh41014
Picked101
Done000
Total10917126

Merged error: 16.4b

Counts
126 → 17

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (sin eps))
0.2b
(* (tan x) (tan eps))
0.2b
(* (* (cos x) (cos eps)) (cos x))
2.6b
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×tan-quot
3×*-commutative
2×associate-*l/ unswap-sqr
1×frac-times sub-neg flip3-- diff-log associate-*r/ cos-mult frac-sub sin-cos-mult flip--
Counts
4 → 71
Calls
4 calls:
5.0ms
(* (cos x) (sin eps))
5.0ms
(* (tan x) (tan eps))
6.0ms
(* (* (cos x) (cos eps)) (cos x))
12.0ms
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

series535.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cos x) (sin eps))
88.0ms
(* (tan x) (tan eps))
47.0ms
(* (* (cos x) (cos eps)) (cos x))
358.0ms
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

simplify49.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0426776
11663688
25001673

prune254.0ms

Filtered
83 candidates to 59 candidates (71.1%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New80383
Fresh21416
Picked101
Done000
Total8317100

Merged error: 16.4b

Counts
100 → 17

regimes179.0ms

bsearch3.0ms

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