Details

Time bar (total: 13.7s)

sample176.0ms

Algorithm
intervals
Results
100.0ms126×body1280valid
26.0ms60×body640valid
12.0ms256×pre80true
7.0ms23×body320valid
4.0ms37×body80valid
2.0ms10×body160valid

simplify22.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 12.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))
3.8b
(tan (+ y z))

rewrite24.0ms

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
(+ x (- (tan (+ y z)) (tan a)))
9.0ms
(- (tan (+ y z)) (tan a))
3.0ms
(tan (+ y z))

series331.0ms

Counts
3 → 9
Calls
3 calls:
136.0ms
(+ x (- (tan (+ y z)) (tan a)))
131.0ms
(- (tan (+ y z)) (tan a))
64.0ms
(tan (+ y z))

simplify96.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
0276685
1732540
23128507
35001488

prune237.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

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

rewrite158.0ms

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:
4.0ms
(+ (tan y) (tan z))
84.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
54.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms
(* (tan y) (tan z))

series1.2s

Counts
4 → 12
Calls
4 calls:
259.0ms
(+ (tan y) (tan z))
374.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
418.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
103.0ms
(* (tan y) (tan z))

simplify83.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06764072
120873376
250013265

prune669.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.3b
(* (tan a) (tan a))
0.4b
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
1.4b
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
108×*-un-lft-identity
80×times-frac
72×add-sqr-sqrt
56×add-cube-cbrt
27×swap-sqr
24×associate-*r* associate-*l*
23×distribute-lft-out
22×add-exp-log add-cbrt-cube
21×tan-quot
20×pow1
11×associate-/r/ associate-/l/
9×frac-times associate-*r/ associate-*l/ frac-sub
6×prod-exp cbrt-unprod unswap-sqr
5×cbrt-undiv flip3-- div-exp flip-- div-inv difference-of-squares
4×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
3×pow-prod-down *-commutative
2×pow2 pow-plus pow-sqr pow-prod-up
1×frac-2neg flip3-+ div-sub frac-add clear-num flip-+
Counts
4 → 196
Calls
4 calls:
6.0ms
(* (tan y) (tan z))
6.0ms
(* (tan a) (tan a))
40.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
82.0ms
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

series1.7s

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (tan y) (tan z))
37.0ms
(* (tan a) (tan a))
251.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
1.3s
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010074613
150014280

prune741.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (+ (tan y) (tan z)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (fma (tan y) (tan z) 1) (+ (- (tan a)) x))
0.2b
(* (tan y) (tan z))
0.2b
(* (tan y) (tan z))
0.3b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
40×tan-quot
20×add-exp-log add-cbrt-cube
19×frac-times pow-prod-down
13×associate-*r/ associate-*l/
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×add-cube-cbrt *-un-lft-identity
7×associate-*r* associate-*l*
4×expm1-log1p-u pow-sqr pow-prod-up log1p-expm1-u add-log-exp
3×*-commutative
2×pow-plus unswap-sqr
1×pow2 swap-sqr fma-udef
Counts
4 → 107
Calls
4 calls:
0.0ms
(fma (/ (+ (tan y) (tan z)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (fma (tan y) (tan z) 1) (+ (- (tan a)) x))
6.0ms
(* (tan y) (tan z))
6.0ms
(* (tan y) (tan z))
28.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series2.2s

Counts
4 → 12
Calls
4 calls:
1.9s
(fma (/ (+ (tan y) (tan z)) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (fma (tan y) (tan z) 1) (+ (- (tan a)) x))
103.0ms
(* (tan y) (tan z))
103.0ms
(* (tan y) (tan z))
128.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify57.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04191096
11863946
25001925

prune466.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes232.0ms

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
02433
12433

end0.0ms

sample5.0s

Algorithm
intervals
Results
3.1s3961×body1280valid
854.0ms1922×body640valid
337.0ms8000×pre80true
211.0ms682×body320valid
110.0ms1154×body80valid
57.0ms281×body160valid