Details

Time bar (total: 12.2s)

sample178.0ms

Algorithm
intervals
Results
92.0ms118×body1280valid
31.0ms70×body640valid
12.0ms256×pre80true
10.0ms8×body160valid
6.0ms21×body320valid
4.0ms39×body80valid

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0155
1225
2335
3395
4505
5705
6995
71245
81665
92595
102605
112605

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.2b
(- (tan (+ y z)) (tan a))
3.3b
(tan (+ y z))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
18×prod-diff
17×add-cube-cbrt
11×associate-+r+
10×add-log-exp
4×tan-quot
3×pow1 add-exp-log expm1-log1p-u fma-def fma-neg add-cbrt-cube log1p-expm1-u
2×sub-neg tan-sum diff-log sum-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 72
Calls
3 calls:
9.0ms
(+ x (- (tan (+ y z)) (tan a)))
9.0ms
(- (tan (+ y z)) (tan a))
4.0ms
(tan (+ y z))

series323.0ms

Counts
3 → 9
Calls
3 calls:
132.0ms
(+ x (- (tan (+ y z)) (tan a)))
128.0ms
(- (tan (+ y z)) (tan a))
63.0ms
(tan (+ y z))

simplify100.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
0276685
1732540
23128507
35001488

prune273.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.3b
(* (tan y) (tan z))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
165×*-un-lft-identity
115×add-sqr-sqrt
108×add-cube-cbrt prod-diff
97×times-frac
56×associate-+r+
27×distribute-lft-out
18×fma-neg
16×associate-/r/
11×add-log-exp
9×flip3-- flip--
8×add-exp-log add-cbrt-cube div-inv
7×tan-quot
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-def associate-*r* associate-*l* associate-/r* associate-/l/
2×sub-neg flip3-+ diff-log sum-log flip-+ distribute-lft-out-- difference-of-squares
1×cbrt-undiv +-commutative frac-times associate-+r- frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ frac-add prod-exp clear-num *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 227
Calls
4 calls:
12.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
89.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
58.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms
(* (tan y) (tan z))

series1.2s

Counts
4 → 12
Calls
4 calls:
231.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
382.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
436.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
108.0ms
(* (tan y) (tan z))

simplify82.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
07044504
122933782
250023674

prune771.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin y) (sin z))
0.2b
(- (+ (/ (sin y) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos y))) (/ (sin z) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos z)))) (/ (sin a) (cos a)))
0.3b
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
0.3b
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

rewrite352.0ms

Algorithm
rewrite-expression-head
Rules
130×*-un-lft-identity
94×times-frac
91×prod-diff
76×add-sqr-sqrt
69×add-cube-cbrt
58×associate-/r/
56×associate-*l/
30×add-exp-log add-cbrt-cube
29×flip3-- flip-- distribute-lft-out
28×distribute-rgt-out
9×prod-exp cbrt-unprod div-inv add-log-exp
8×cbrt-undiv div-exp
7×fma-neg
6×pow1
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* associate-*l* frac-sub sin-mult
2×frac-2neg diff-log clear-num associate-/r* cos-mult associate-/l/ associate-/l* distribute-lft-out-- difference-of-squares
1×sub-neg flip3-+ pow-prod-down frac-add associate--l+ sum-log *-commutative flip-+ unswap-sqr
Counts
4 → 192
Calls
4 calls:
4.0ms
(* (sin y) (sin z))
323.0ms
(- (+ (/ (sin y) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos y))) (/ (sin z) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos z)))) (/ (sin a) (cos a)))
6.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
6.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series692.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin y) (sin z))
432.0ms
(- (+ (/ (sin y) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos y))) (/ (sin z) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos z)))) (/ (sin a) (cos a)))
105.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
107.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify146.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
08958686
137307019
250026886

prune801.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin y) (sin z))
0.2b
(/ (sin z) (cos z))
0.2b
(- (* (/ 1 (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (+ (/ (sin y) (cos y)) (/ (sin z) (cos z)))) (/ (sin a) (cos a)))
0.3b
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
20×add-exp-log add-cbrt-cube
19×times-frac
13×prod-diff
7×frac-sub
6×pow1 add-log-exp
5×cbrt-undiv div-exp prod-exp cbrt-unprod
4×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
3×frac-times associate-*r/ associate-*r* associate-*l* div-inv
2×frac-2neg flip3-+ frac-add associate--l+ clear-num flip-+ sin-mult
1×distribute-rgt-in sub-neg quot-tan flip3-- distribute-lft-in fma-neg diff-log pow-prod-down associate-*l/ associate-/r/ cos-mult *-commutative flip-- associate-/l/ unswap-sqr
Counts
4 → 113
Calls
4 calls:
4.0ms
(* (sin y) (sin z))
3.0ms
(/ (sin z) (cos z))
38.0ms
(- (* (/ 1 (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (+ (/ (sin y) (cos y)) (/ (sin z) (cos z)))) (/ (sin a) (cos a)))
6.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series617.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (sin y) (sin z))
22.0ms
(/ (sin z) (cos z))
432.0ms
(- (* (/ 1 (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (+ (/ (sin y) (cos y)) (/ (sin z) (cos z)))) (/ (sin a) (cos a)))
107.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify107.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
08892086
139291743
250021699

prune620.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03729
13729

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.1s3877×body1280valid
880.0ms1952×body640valid
382.0ms8000×pre80true
226.0ms734×body320valid
118.0ms1166×body80valid
57.0ms271×body160valid