Details

Time bar (total: 10.8s)

sample168.0ms

Algorithm
intervals
Results
95.0ms121×body1280valid
27.0ms66×body640valid
10.0ms256×pre80true
5.0ms18×body320valid
3.0ms38×body80valid
3.0ms13×body160valid

simplify21.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(- (tan (+ y z)) (tan a))
0.2b
(+ x (- (tan (+ y z)) (tan a)))
2.4b
(tan (+ y z))

rewrite22.0ms

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:
8.0ms
(- (tan (+ y z)) (tan a))
8.0ms
(+ x (- (tan (+ y z)) (tan a)))
3.0ms
(tan (+ y z))

series286.0ms

Counts
3 → 9
Calls
3 calls:
116.0ms
(- (tan (+ y z)) (tan a))
116.0ms
(+ x (- (tan (+ y z)) (tan a)))
54.0ms
(tan (+ y z))

simplify94.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
0276685
1732540
23057507
35001488

prune252.0ms

Filtered
81 candidates to 59 candidates (72.8%)
Pruning

10 alts after pruning (10 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)))) (tan a))
0.1b
(+ (tan y) (tan z))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b
(* (tan y) (tan z))

rewrite154.0ms

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:
52.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
3.0ms
(+ (tan y) (tan z))
82.0ms
(+ x (- (/ (+ (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:
422.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
102.0ms
(+ (tan y) (tan z))
372.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
104.0ms
(* (tan y) (tan z))

simplify83.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06764072
120873376
250023151

prune700.0ms

Filtered
219 candidates to 132 candidates (60.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (tan a))
0.6b
(cbrt (tan a))
0.6b
(cbrt (tan a))
59.4b
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×tan-quot cbrt-div pow1/3
1×fma-udef
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt (tan a))
1.0ms
(cbrt (tan a))
1.0ms
(cbrt (tan a))
0.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series613.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(cbrt (tan a))
131.0ms
(cbrt (tan a))
131.0ms
(cbrt (tan a))
212.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify107.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 4 (102.0ms)

IterNodesCost
0102427
1211373
2675363
32633349
45002337

prune377.0ms

Filtered
64 candidates to 57 candidates (89.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (tan y) (tan z)) (cos 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)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
14×tan-quot *-un-lft-identity
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×associate-/l/
6×frac-sub
5×flip3-- flip--
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×flip3-+ times-frac pow-prod-down frac-add *-commutative flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp associate-/r/
1×frac-2neg div-sub clear-num associate-/r* div-inv distribute-lft-out
Counts
4 → 104
Calls
4 calls:
12.0ms
(* (+ (tan y) (tan z)) (cos a))
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))
23.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series893.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(* (+ (tan y) (tan z)) (cos a))
104.0ms
(* (tan y) (tan z))
105.0ms
(* (tan y) (tan z))
523.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify80.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06071365
128351198
250011191

prune531.0ms

Filtered
116 candidates to 91 candidates (78.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes269.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02729
12729

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.0s3877×body1280valid
895.0ms1986×body640valid
345.0ms8000×pre80true
215.0ms711×body320valid
109.0ms1150×body80valid
57.0ms276×body160valid