Details

Time bar (total: 19.3s)

sample111.0ms

Algorithm
intervals
Results
53.0ms120×body1280valid
17.0ms67×body640valid
14.0ms256×pre80true
4.0ms25×body320valid
2.0ms32×body80valid
1.0ms12×body160valid

simplify30.0ms

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

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.6b

Counts
2 → 1

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))
2.6b
(tan (+ y z))

rewrite21.0ms

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
5×tan-quot
4×tan-sum
3×pow1 add-exp-log +-commutative expm1-log1p-u fma-def fma-neg frac-sub add-cbrt-cube log1p-expm1-u
2×sub-neg diff-log sum-log distribute-lft-out distribute-lft-out--
1×associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 74
Calls
3 calls:
7.0ms
(+ x (- (tan (+ y z)) (tan a)))
7.0ms
(- (tan (+ y z)) (tan a))
4.0ms
(tan (+ y z))

series326.0ms

Counts
3 → 9
Calls
3 calls:
137.0ms
(+ x (- (tan (+ y z)) (tan a)))
128.0ms
(- (tan (+ y z)) (tan a))
61.0ms
(tan (+ y z))

simplify105.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0286710
1726565
23028532
35001471

prune164.0ms

Filtered
83 candidates to 55 candidates (33.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New731083
Fresh000
Picked101
Done000
Total741084

Merged error: 0.1b

Counts
84 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
503×*-un-lft-identity
431×add-sqr-sqrt
253×times-frac
252×prod-diff
192×add-cube-cbrt
128×associate-+r+
118×difference-of-squares
67×distribute-lft-out
60×distribute-lft-out--
59×unswap-sqr
42×fma-neg
32×associate-*l*
27×tan-quot
19×frac-sub
14×associate-/r/
13×add-log-exp
9×associate-/r*
8×flip3-- flip--
7×div-inv
6×pow1 add-exp-log fma-def add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×flip3-+ associate-*r* sum-log flip-+ associate-/l/
2×+-commutative sub-neg diff-log frac-add
1×frac-times associate-+r- frac-2neg associate-*r/ pow-prod-down associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 393
Calls
4 calls:
5.0ms
(+ (tan y) (tan z))
38.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
33.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
6.0ms
(* (tan z) (tan y))

series1.1s

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (tan y) (tan z))
400.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
449.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
115.0ms
(* (tan z) (tan y))

simplify154.0ms

Algorithm
egg-herbie
Counts
405 → 405
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
010748767
134977164
250026904

prune780.0ms

Filtered
405 candidates to 180 candidates (55.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New39411405
Fresh909
Picked101
Done000
Total40411415

Merged error: 0.0b

Counts
415 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
136×add-sqr-sqrt
108×*-un-lft-identity
102×associate-*l*
93×times-frac
60×add-cube-cbrt
36×distribute-lft-neg-in distribute-rgt-neg-in
32×difference-of-squares
31×associate-/r*
22×unswap-sqr
18×associate-*r*
16×distribute-lft-out--
13×add-exp-log add-cbrt-cube
8×tan-quot pow1
6×*-commutative
4×expm1-log1p-u neg-mul-1 associate-*l/ log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv frac-times associate-*r/ div-exp pow-prod-down associate-/r/ distribute-neg-frac
1×flip3-- frac-2neg clear-num flip-- fma-udef div-inv
Counts
4 → 201
Calls
4 calls:
1.0ms
(fma (- (+ (tan y) (tan z))) (cos a) (* (- 1 (* (tan z) (tan y))) (sin a)))
19.0ms
(/ (fma (- (+ (tan y) (tan z))) (cos a) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- (- 1 (* (tan z) (tan y)))) (cos a)))
5.0ms
(* (tan z) (tan y))
5.0ms
(* (tan z) (tan y))

series1.0s

Counts
4 → 12
Calls
4 calls:
308.0ms
(fma (- (+ (tan y) (tan z))) (cos a) (* (- 1 (* (tan z) (tan y))) (sin a)))
501.0ms
(/ (fma (- (+ (tan y) (tan z))) (cos a) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- (- 1 (* (tan z) (tan y)))) (cos a)))
98.0ms
(* (tan z) (tan y))
103.0ms
(* (tan z) (tan y))

simplify111.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07735401
127665207
250025188

prune716.0ms

Filtered
213 candidates to 148 candidates (30.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2130213
Fresh01010
Picked011
Done000
Total21311224

Merged error: 0.0b

Counts
224 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan z) (tan y))
0.3b
(* (tan a) (tan a))
0.4b
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))))
0.6b
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))

rewrite915.0ms

Algorithm
rewrite-expression-head
Rules
2627×add-sqr-sqrt
2357×*-un-lft-identity
1957×tan-quot
1848×frac-times
1691×associate-/l/
1453×associate-/r*
1206×frac-sub
949×difference-of-squares
705×associate-/l*
618×times-frac
513×unswap-sqr
480×associate-*r/ associate-*l/
463×add-cube-cbrt
435×distribute-lft-out--
297×distribute-lft-out
273×associate-*l*
204×swap-sqr
180×frac-add
166×clear-num
162×frac-2neg flip3-+ flip-+
73×*-commutative
48×associate-*r*
29×associate-/r/
22×add-exp-log add-cbrt-cube
20×pow1
12×un-div-inv
6×prod-exp cbrt-unprod
5×cbrt-undiv flip3-- div-exp flip-- div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
2×pow2 pow-plus pow-sqr pow-prod-up
1×div-sub
Counts
4 → 2175
Calls
4 calls:
5.0ms
(* (tan z) (tan y))
5.0ms
(* (tan a) (tan a))
70.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))))
532.0ms
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))

series1.7s

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (tan z) (tan y))
37.0ms
(* (tan a) (tan a))
242.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))))
1.3s
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))

simplify514.0ms

Algorithm
egg-herbie
Counts
2187 → 2187
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0500162715

prune7.9s

Filtered
2187 candidates to 1205 candidates (44.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New218612187
Fresh189
Picked101
Done011
Total2188102198

Merged error: 0.0b

Counts
2198 → 10

regimes385.0ms

Accuracy

0% (0.1b 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
03121
13621
23721
33721

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.6s3927×body1280valid
480.0ms2030×body640valid
319.0ms8000×pre80true
111.0ms656×body320valid
54.0ms1085×body80valid
33.0ms302×body160valid