Details

Time bar (total: 16.1s)

sample308.0ms

Algorithm
intervals
Results
166.0ms96×body1280valid
62.0ms24×body2560valid
39.0ms56×body640valid
20.0ms39×body320valid
5.0ms31×body80valid
3.0ms10×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize10.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (tan (+ x eps)) (tan x))
6.3b
(tan (+ x eps))

rewrite38.0ms

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:
30.0ms
(- (tan (+ x eps)) (tan x))
7.0ms
(tan (+ x eps))

series261.0ms

Counts
2 → 6
Calls
2 calls:
148.0ms
(- (tan (+ x eps)) (tan x))
113.0ms
(tan (+ x eps))

simplify2.6s

Counts
31 → 31
Iterations

Useful iterations: 4 (340.0ms)

IterNodesCost
068367
1135355
2278341
3528337
41109335
52471335
done5000335

prune119.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize27.0ms

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))
2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite212.0ms

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:
47.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
19.0ms
(+ (tan x) (tan eps))
31.0ms
(* (tan x) (tan eps))
113.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
347.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
148.0ms
(+ (tan x) (tan eps))
163.0ms
(* (tan x) (tan eps))
536.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.3s

Counts
98 → 98
Iterations

Useful iterations: 3 (922.0ms)

IterNodesCost
01721724
13971649
210951579
329391563
done50001563

prune411.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.9b

localize32.0ms

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))
2.4b
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite172.0ms

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:
9.0ms
(+ (tan x) (tan eps))
88.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
31.0ms
(* (tan x) (tan eps))
40.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series1.3s

Counts
4 → 12
Calls
4 calls:
164.0ms
(+ (tan x) (tan eps))
381.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
155.0ms
(* (tan x) (tan eps))
612.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify1.7s

Counts
111 → 111
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02252170
15501939
216511820
done50001796

prune541.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (cos x) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))) (* (* (cos x) (cos eps)) (cos x)))
0.2b
(* (tan x) (tan eps))
0.2b
(* (* (cos x) (cos eps)) (cos x))
2.4b
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

rewrite525.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
13×prod-exp cbrt-unprod
11×pow1
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-undiv div-exp associate-*r* add-log-exp
4×tan-quot associate-*r/ associate-*l* pow-prod-down
3×associate-*l/ associate-/l/
2×flip3-- cos-mult *-commutative frac-sub sin-cos-mult flip--
1×frac-times sub-neg frac-2neg times-frac diff-log clear-num associate-/r* associate-/r/ div-inv associate-/l* unswap-sqr
Counts
4 → 82
Calls
4 calls:
273.0ms
(/ (* (cos x) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))) (* (* (cos x) (cos eps)) (cos x)))
25.0ms
(* (tan x) (tan eps))
49.0ms
(* (* (cos x) (cos eps)) (cos x))
173.0ms
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

series1.4s

Counts
4 → 12
Calls
4 calls:
621.0ms
(/ (* (cos x) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))) (* (* (cos x) (cos eps)) (cos x)))
123.0ms
(* (tan x) (tan eps))
53.0ms
(* (* (cos x) (cos eps)) (cos x))
636.0ms
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))

simplify2.0s

Counts
94 → 94
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01872861
15502801
224112069
done50002061

prune446.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.9b

regimes282.0ms

bsearch3.0ms