Details

Time bar (total: 11.8s)

sample204.0ms

Algorithm
intervals
Results
103.0ms118×body1280valid
35.0ms70×body640valid
25.0ms256×pre80true
8.0ms39×body80valid
7.0ms21×body320valid
2.0ms8×body160valid

simplify21.0ms

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: 12.2b

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))
3.3b
(tan (+ y z))

rewrite18.0ms

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:
7.0ms
(+ x (- (tan (+ y z)) (tan a)))
7.0ms
(- (tan (+ y z)) (tan a))
3.0ms
(tan (+ y z))

series299.0ms

Counts
3 → 9
Calls
3 calls:
123.0ms
(+ x (- (tan (+ y z)) (tan a)))
118.0ms
(- (tan (+ y z)) (tan a))
58.0ms
(tan (+ y z))

simplify40.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0196346
1467335
21316334
35002334

prune166.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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))
0.3b
(* (tan y) (tan z))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
11×add-log-exp
8×add-exp-log add-cbrt-cube
7×tan-quot
6×pow1 distribute-lft-out
4×associate-/l*
3×associate-*r* associate-*l* associate-/r* associate-/l/
2×sub-neg associate-+r+ flip3-- flip3-+ diff-log sum-log associate-/r/ flip-- 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 div-inv unswap-sqr
Counts
4 → 90
Calls
4 calls:
11.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
68.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
41.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms
(* (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
556.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
400.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
95.0ms
(* (tan y) (tan z))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04491259
115031211
250011204

prune361.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
11×*-un-lft-identity
9×prod-exp cbrt-unprod add-log-exp
8×cbrt-undiv div-exp
6×pow1 add-cube-cbrt
3×times-frac associate-*r* associate-*l* frac-sub sin-mult
2×frac-2neg diff-log clear-num associate-/r* associate-/r/ cos-mult div-inv associate-/l/ associate-/l* distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip3-+ pow-prod-down frac-add associate--l+ sum-log *-commutative flip-- flip-+ distribute-lft-out unswap-sqr
Counts
4 → 86
Calls
4 calls:
4.0ms
(* (sin y) (sin z))
239.0ms
(- (+ (/ (sin y) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos y))) (/ (sin z) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos z)))) (/ (sin a) (cos a)))
5.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
6.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

series642.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin y) (sin z))
397.0ms
(- (+ (/ (sin y) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos y))) (/ (sin z) (* (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cos z)))) (/ (sin a) (cos a)))
98.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
99.0ms
(/ (* (sin y) (sin z)) (* (cos z) (cos y)))

simplify61.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04561842
120931605
250021605

prune438.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y)))))
6.8b
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
6.8b
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
6.8b
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
46×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3 swap-sqr associate-*r* associate-*l*
7×cbrt-div times-frac associate-/r/ cos-mult div-inv
6×add-exp-log
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 97
Calls
4 calls:
14.0ms
(* (cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y)))))
3.0ms
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
3.0ms
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
3.0ms
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))

series663.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(* (cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y)))) (cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y)))))
155.0ms
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
151.0ms
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))
157.0ms
(cbrt (/ (* (sin y) (sin z)) (* (cos z) (cos y))))

simplify45.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02481658
110251466
250021359

prune630.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes360.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03649
13649

end0.0ms

sample6.0s

Algorithm
intervals
Results
3.3s3877×body1280valid
1.0s1952×body640valid
763.0ms8000×pre80true
276.0ms734×body320valid
181.0ms1166×body80valid
71.0ms271×body160valid