Details

Time bar (total: 18.2s)

sample100.0ms

Algorithm
intervals
Results
43.0ms107×body1280valid
15.0ms69×body640valid
10.0ms256×pre80true
4.0ms28×body320valid
2.0ms39×body80valid
1.0ms13×body160valid

simplify20.0ms

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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 10.7b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.2b
(- (tan (+ y z)) (tan a))
3.1b
(tan (+ y z))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
2×sub-neg tan-sum associate-+r+ 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 → 42
Calls
3 calls:
5.0ms
(+ x (- (tan (+ y z)) (tan a)))
6.0ms
(- (tan (+ y z)) (tan a))
4.0ms
(tan (+ y z))

series288.0ms

Counts
3 → 9
Calls
3 calls:
121.0ms
(+ x (- (tan (+ y z)) (tan a)))
113.0ms
(- (tan (+ y z)) (tan a))
54.0ms
(tan (+ y z))

simplify42.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0196346
1467335
21316334
35002334

prune144.0ms

Filtered
51 candidates to 39 candidates (76.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New44751
Fresh000
Picked101
Done000
Total45752

Merged error: 0.1b

Counts
52 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×tan-quot
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
12×frac-sub
10×add-cube-cbrt *-un-lft-identity
9×flip3-- flip--
8×pow1 associate-/l/
6×associate-*r* associate-*l* add-log-exp
4×flip3-+ frac-add flip-+
3×times-frac prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv frac-times associate-*r/ div-exp pow-prod-down associate-/r/ *-commutative unswap-sqr
1×sub-neg frac-2neg diff-log div-sub clear-num associate-/r* div-inv
Counts
4 → 92
Calls
4 calls:
9.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))
15.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series964.0ms

Counts
4 → 12
Calls
4 calls:
296.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
94.0ms
(* (tan y) (tan z))
95.0ms
(* (tan y) (tan z))
479.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify85.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06551681
130931507
250011490

prune458.0ms

Filtered
104 candidates to 83 candidates (79.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New995104
Fresh156
Picked101
Done000
Total10110111

Merged error: 0.0b

Counts
111 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.2b
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
0.2b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b
(pow (* (tan y) (tan z)) 3)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
44×tan-quot
27×associate-*l/
26×add-exp-log add-cbrt-cube
19×frac-times pow-prod-down
13×associate-*r/
11×add-sqr-sqrt prod-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity
8×associate-/l/
6×frac-sub
5×flip3-- flip--
4×associate-*r* associate-*l* pow-sqr pow-prod-up add-log-exp
3×cube-div pow-unpow times-frac associate-/l*
2×cbrt-undiv pow-pow flip3-+ pow-plus div-exp frac-add pow-exp associate-/r/ *-commutative flip-+ rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down frac-2neg unpow3 div-sub cube-prod swap-sqr clear-num associate-/r* div-inv unswap-sqr sqr-pow
Counts
4 → 127
Calls
4 calls:
5.0ms
(* (tan y) (tan z))
17.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
11.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
6.0ms
(pow (* (tan y) (tan z)) 3)

series862.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (tan y) (tan z))
529.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
113.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
125.0ms
(pow (* (tan y) (tan z)) 3)

simplify127.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
08121495
144531335
250011331

prune557.0ms

Filtered
139 candidates to 88 candidates (63.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1390139
Fresh099
Picked011
Done000
Total13910149

Merged error: 0.0b

Counts
149 → 10

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan z) (tan z))
0.3b
(pow (* (tan y) (tan z)) 3)
0.3b
(* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))
1.6b
(/ (- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))) (* (* (+ (* (* (tan y) (tan z)) (+ (* (tan y) (tan z)) 1)) 1) (- (tan y) (tan z))) (* (- 1 (* (tan y) (tan z))) (cos a))))

rewrite398.0ms

Algorithm
rewrite-expression-head
Rules
1137×associate-*l/
1050×tan-quot
807×frac-sub
698×frac-times
391×associate-/l/
309×associate-*r/
307×flip3-- flip--
144×flip3-+ flip-+
35×associate-/r/
32×add-exp-log add-cbrt-cube
19×pow1
16×add-sqr-sqrt
14×*-un-lft-identity
13×prod-exp cbrt-unprod
12×add-cube-cbrt
8×associate-*l*
5×cbrt-undiv div-exp pow-prod-down
4×associate-*r* sub-div add-log-exp
3×cube-div pow-unpow times-frac swap-sqr associate-/l*
2×pow-pow pow-exp *-commutative rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down frac-2neg pow-plus unpow3 div-sub cube-prod clear-num associate-/r* pow-sqr pow-prod-up div-inv distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 538
Calls
4 calls:
5.0ms
(* (tan z) (tan z))
6.0ms
(pow (* (tan y) (tan z)) 3)
19.0ms
(* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))
271.0ms
(/ (- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))) (* (* (+ (* (* (tan y) (tan z)) (+ (* (tan y) (tan z)) 1)) 1) (- (tan y) (tan z))) (* (- 1 (* (tan y) (tan z))) (cos a))))

series2.5s

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (tan z) (tan z))
120.0ms
(pow (* (tan y) (tan z)) 3)
293.0ms
(* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))
2.0s
(/ (- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a)))) (* (* (+ (* (* (tan y) (tan z)) (+ (* (tan y) (tan z)) 1)) 1) (- (tan y) (tan z))) (* (- 1 (* (tan y) (tan z))) (cos a))))

simplify267.0ms

Algorithm
egg-herbie
Counts
550 → 550
Iterations

Useful iterations: 1 (79.0ms)

IterNodesCost
0403625578
1500225310

prune7.7s

Filtered
550 candidates to 512 candidates (93.1%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5500550
Fresh088
Picked011
Done011
Total55010560

Merged error: 0.0b

Counts
560 → 10

regimes604.0ms

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
03935
14435
24435

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.6s3855×body1280valid
480.0ms2051×body640valid
313.0ms8000×pre80true
111.0ms708×body320valid
51.0ms1113×body80valid
29.0ms273×body160valid