Details

Time bar (total: 10.7s)

sample122.0ms

Algorithm
intervals
Results
47.0ms112×body1280valid
24.0ms256×pre80true
16.0ms61×body640valid
6.0ms33×body320valid
2.0ms41×body80valid
1.0ms9×body160valid

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

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: 11.1b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(- (tan (+ y z)) (tan a))
0.2b
(+ x (- (tan (+ y z)) (tan a)))
3.7b
(tan (+ y z))

rewrite29.0ms

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
(- (tan (+ y z)) (tan a))
12.0ms
(+ x (- (tan (+ y z)) (tan a)))
5.0ms
(tan (+ y z))

series314.0ms

Counts
3 → 9
Calls
3 calls:
128.0ms
(- (tan (+ y z)) (tan a))
131.0ms
(+ x (- (tan (+ y z)) (tan a)))
55.0ms
(tan (+ y z))

simplify96.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
0276685
1732540
23057507
35001488

prune263.0ms

Filtered
81 candidates to 59 candidates (72.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New72981
Fresh000
Picked101
Done000
Total73982

Merged error: 0.1b

Counts
82 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
151×*-un-lft-identity
108×prod-diff
107×add-sqr-sqrt
100×add-cube-cbrt
85×times-frac
56×associate-+r+
24×distribute-lft-out
18×fma-neg
14×associate-/r/
13×add-log-exp
8×flip3-- flip--
7×tan-quot div-inv
6×pow1 add-exp-log fma-def add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* associate-*l* sum-log
2×+-commutative sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- associate-*r/ pow-prod-down associate-*l/ frac-add prod-exp *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 207
Calls
4 calls:
6.0ms
(+ (tan y) (tan z))
22.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
22.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms
(* (tan y) (tan z))

series1.0s

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (tan y) (tan z))
388.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
425.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
99.0ms
(* (tan y) (tan z))

simplify88.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06764072
120873376
250013265

prune666.0ms

Filtered
219 candidates to 132 candidates (60.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2163219
Fresh088
Picked101
Done000
Total21711228

Merged error: 0.1b

Counts
228 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
0.2b
(exp (* (tan y) (tan z)))
0.2b
(* (tan y) (tan z))
3.1b
(log (exp (* (tan y) (tan z))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
211×*-un-lft-identity
144×add-sqr-sqrt
113×times-frac
102×prod-diff
89×add-cube-cbrt
34×fma-neg difference-of-squares
33×distribute-lft-out--
28×distribute-lft-out
23×pow1
19×log-pow
9×add-log-exp
8×associate-/r/
6×add-exp-log add-cbrt-cube
5×tan-quot flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×log-prod associate-*r* associate-*l*
2×exp-prod exp-to-pow
1×frac-times sub-neg diff-log associate-*r/ rem-log-exp pow-prod-down associate-*l/ prod-exp *-commutative frac-sub cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 205
Calls
4 calls:
28.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
4.0ms
(exp (* (tan y) (tan z)))
6.0ms
(* (tan y) (tan z))
2.0ms
(log (exp (* (tan y) (tan z))))

series988.0ms

Counts
4 → 12
Calls
4 calls:
411.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
376.0ms
(exp (* (tan y) (tan z)))
101.0ms
(* (tan y) (tan z))
99.0ms
(log (exp (* (tan y) (tan z))))

simplify85.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05424427
116843338
250013278

prune531.0ms

Filtered
217 candidates to 97 candidates (44.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2170217
Fresh01010
Picked011
Done000
Total21711228

Merged error: 0.1b

Counts
228 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
321×*-un-lft-identity
237×add-sqr-sqrt
180×prod-diff
172×times-frac
146×add-cube-cbrt
92×associate-+r+
58×difference-of-squares
44×distribute-lft-out
30×fma-neg distribute-lft-out--
14×associate-/r/
11×add-exp-log add-cbrt-cube add-log-exp
8×flip3-- flip-- div-inv
6×pow1
4×expm1-log1p-u log1p-expm1-u
3×tan-quot fma-def associate-*r* associate-*l* associate-/r*
2×cbrt-undiv sub-neg diff-log div-exp associate-*l/ prod-exp sum-log cbrt-unprod
1×+-commutative associate-+r- frac-2neg flip3-+ pow-prod-down clear-num *-commutative frac-sub flip-+ associate-/l/ associate-/l* unswap-sqr
Counts
4 → 295
Calls
4 calls:
7.0ms
(/ (* (tan y) (sin z)) (cos z))
32.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
31.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
7.0ms
(* (tan y) (sin z))

series1.0s

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (* (tan y) (sin z)) (cos z))
396.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
428.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
79.0ms
(* (tan y) (sin z))

simplify114.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
08047024
125815848
250025662

prune895.0ms

Filtered
307 candidates to 150 candidates (48.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3061307
Fresh189
Picked101
Done011
Total30810318

Merged error: 0.0b

Counts
318 → 10

regimes692.0ms

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
02113
12113

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.8s3862×body1280valid
568.0ms8000×pre80true
541.0ms2021×body640valid
130.0ms690×body320valid
69.0ms1151×body80valid
36.0ms276×body160valid