Details

Time bar (total: 14.8s)

sample170.0ms

Algorithm
intervals
Results
86.0ms118×body1280valid
33.0ms61×body640valid
10.0ms256×pre80true
8.0ms30×body320valid
3.0ms37×body80valid
2.0ms10×body160valid

simplify24.0ms

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: 13.8b

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))
4.4b
(tan (+ y z))

rewrite50.0ms

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:
22.0ms
(+ x (- (tan (+ y z)) (tan a)))
18.0ms
(- (tan (+ y z)) (tan a))
7.0ms
(tan (+ y z))

series357.0ms

Counts
3 → 9
Calls
3 calls:
155.0ms
(+ x (- (tan (+ y z)) (tan a)))
141.0ms
(- (tan (+ y z)) (tan a))
61.0ms
(tan (+ y z))

simplify98.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
0276685
1732540
23128507
35001488

prune239.0ms

Pruning

6 alts after pruning (6 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))
0.2b
(* (tan y) (tan z))

rewrite310.0ms

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:
31.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
149.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
101.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
16.0ms
(* (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
269.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
439.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
482.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
116.0ms
(* (tan y) (tan z))

simplify92.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
07044490
122933769
250023667

prune742.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
41×tan-quot
37×add-sqr-sqrt
33×*-un-lft-identity prod-diff
27×add-cube-cbrt
20×add-exp-log times-frac add-cbrt-cube
19×frac-times pow-prod-down
13×associate-*r/ associate-*l/
11×fma-neg
10×prod-exp cbrt-unprod
9×difference-of-squares
8×associate-/r/
7×associate-*r* associate-*l*
6×add-log-exp
5×flip3-- flip--
4×expm1-log1p-u pow-sqr pow-prod-up log1p-expm1-u div-inv
3×*-commutative
2×pow-plus unswap-sqr
1×pow2 sub-neg diff-log swap-sqr frac-sub distribute-lft-out--
Counts
4 → 158
Calls
4 calls:
59.0ms
(- (/ (* (+ (tan y) (tan z)) (fma (tan y) (tan z) 1)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (tan a))
15.0ms
(* (tan y) (tan z))
15.0ms
(* (tan y) (tan z))
72.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series1.5s

Counts
4 → 12
Calls
4 calls:
1.1s
(- (/ (* (+ (tan y) (tan z)) (fma (tan y) (tan z) 1)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (tan a))
109.0ms
(* (tan y) (tan z))
109.0ms
(* (tan y) (tan z))
139.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify93.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06502711
128202194
250022186

prune618.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
121×pow1
96×tan-quot
51×frac-times pow-prod-down
40×add-exp-log add-cbrt-cube
33×associate-*r/ associate-*l/
24×prod-exp cbrt-unprod
12×pow-sqr pow-prod-up
6×pow-plus
4×add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity log1p-expm1-u add-log-exp
3×pow2 swap-sqr associate-*r* associate-*l* *-commutative
1×fma-udef
Counts
4 → 163
Calls
4 calls:
0.0ms
(fma (/ (* (+ (tan y) (tan z)) (fma (tan y) (tan z) 1)) (- (* 1 1) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (+ 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (- (tan a)))
69.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
69.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
69.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series2.4s

Counts
4 → 12
Calls
4 calls:
2.0s
(fma (/ (* (+ (tan y) (tan z)) (fma (tan y) (tan z) 1)) (- (* 1 1) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (+ 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (- (tan a)))
142.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
145.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
150.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify83.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
04832064
124771743
250011738

prune825.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes256.0ms

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
03141
13141

end0.0ms

sample5.1s

Algorithm
intervals
Results
3.0s3864×body1280valid
920.0ms2022×body640valid
330.0ms8000×pre80true
192.0ms639×body320valid
104.0ms1175×body80valid
67.0ms300×body160valid