Details

Time bar (total: 14.6s)

sample112.0ms

Algorithm
intervals
Results
54.0ms121×body1280valid
17.0ms73×body640valid
10.0ms256×pre80true
5.0ms25×body320valid
1.0ms28×body80valid
1.0ms9×body160valid

simplify31.0ms

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: 10.6b

Counts
2 → 1

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))
3.5b
(tan (+ y z))

rewrite23.0ms

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
5×tan-quot
4×tan-sum
3×pow1 add-exp-log +-commutative expm1-log1p-u fma-def fma-neg frac-sub add-cbrt-cube log1p-expm1-u
2×sub-neg diff-log sum-log distribute-lft-out distribute-lft-out--
1×associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 74
Calls
3 calls:
7.0ms
(+ x (- (tan (+ y z)) (tan a)))
8.0ms
(- (tan (+ y z)) (tan a))
5.0ms
(tan (+ y z))

series345.0ms

Counts
3 → 9
Calls
3 calls:
143.0ms
(+ x (- (tan (+ y z)) (tan a)))
136.0ms
(- (tan (+ y z)) (tan a))
66.0ms
(tan (+ y z))

simplify107.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0286710
1726565
23028532
35001471

prune170.0ms

Filtered
83 candidates to 55 candidates (66.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New75883
Fresh000
Picked101
Done000
Total76884

Merged error: 0.0b

Counts
84 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
1099×*-un-lft-identity
812×associate-*l*
795×add-sqr-sqrt
426×distribute-lft-out--
342×times-frac
234×prod-diff
212×difference-of-squares
200×unswap-sqr
183×add-cube-cbrt
162×associate-*r*
99×distribute-lft-out
54×*-commutative
28×associate-*l/
19×associate-/l*
18×associate-/r*
16×tan-quot
13×add-exp-log fma-neg add-cbrt-cube
12×frac-sub
9×flip3-- flip--
8×pow1 associate-/l/
6×add-log-exp
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u
3×prod-exp cbrt-unprod
2×cbrt-undiv frac-times associate-*r/ div-exp pow-prod-down associate-/r/
1×sub-neg frac-2neg diff-log div-sub clear-num div-inv
Counts
4 → 735
Calls
4 calls:
38.0ms
(- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))
75.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
6.0ms
(* (tan z) (tan y))
6.0ms
(* (tan z) (tan y))

series1.1s

Counts
4 → 12
Calls
4 calls:
355.0ms
(- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))
558.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
110.0ms
(* (tan z) (tan y))
121.0ms
(* (tan z) (tan y))

simplify225.0ms

Algorithm
egg-herbie
Counts
747 → 747
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0188723855
1500220430

prune1.3s

Filtered
747 candidates to 240 candidates (32.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New7452747
Fresh167
Picked011
Done000
Total7469755

Merged error: 0.0b

Counts
755 → 9

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan z) (tan y))
0.3b
(* (tan y) (tan y))
0.3b
(* (- (tan z) (tan y)) (* (- 1 (* (* (tan z) (tan y)) (* (tan z) (tan y)))) (sin a)))
1.8b
(/ (fma (fma (tan z) (tan y) 1) (* (- (* (tan z) (tan z)) (* (tan y) (tan y))) (cos a)) (- (* (- (tan z) (tan y)) (* (- 1 (* (* (tan z) (tan y)) (* (tan z) (tan y)))) (sin a))))) (* (- (tan z) (tan y)) (+ 1 (* (tan z) (tan y)))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
119×add-sqr-sqrt
84×*-un-lft-identity
62×associate-*r* associate-*l*
48×times-frac
43×add-cube-cbrt
30×unswap-sqr
23×difference-of-squares
20×tan-quot
18×pow1 add-exp-log add-cbrt-cube
16×associate-*l/ associate-/r*
14×frac-times
11×associate-/r/
10×flip3-- *-commutative flip--
8×distribute-lft-out distribute-lft-out--
7×swap-sqr
6×associate-*r/ prod-exp frac-sub cbrt-unprod
5×pow-prod-down
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×associate-/l*
2×cbrt-undiv div-exp
1×pow2 frac-2neg pow-plus clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 214
Calls
4 calls:
6.0ms
(* (tan z) (tan y))
6.0ms
(* (tan y) (tan y))
48.0ms
(* (- (tan z) (tan y)) (* (- 1 (* (* (tan z) (tan y)) (* (tan z) (tan y)))) (sin a)))
20.0ms
(/ (fma (fma (tan z) (tan y) 1) (* (- (* (tan z) (tan z)) (* (tan y) (tan y))) (cos a)) (- (* (- (tan z) (tan y)) (* (- 1 (* (* (tan z) (tan y)) (* (tan z) (tan y)))) (sin a))))) (* (- (tan z) (tan y)) (+ 1 (* (tan z) (tan y)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (tan z) (tan y))
39.0ms
(* (tan y) (tan y))
361.0ms
(* (- (tan z) (tan y)) (* (- 1 (* (* (tan z) (tan y)) (* (tan z) (tan y)))) (sin a)))
1.4s
(/ (fma (fma (tan z) (tan y) 1) (* (- (* (tan z) (tan z)) (* (tan y) (tan y))) (cos a)) (- (* (- (tan z) (tan y)) (* (- 1 (* (* (tan z) (tan y)) (* (tan z) (tan y)))) (sin a))))) (* (- (tan z) (tan y)) (+ 1 (* (tan z) (tan y)))))

simplify97.0ms

Algorithm
egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
012207097
150016774

prune1.4s

Filtered
226 candidates to 161 candidates (71.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2260226
Fresh077
Picked011
Done011
Total2269235

Merged error: 0.0b

Counts
235 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))) (cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))))
0.5b
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))
0.5b
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))
0.5b
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
1093×*-un-lft-identity
642×associate-*l*
558×distribute-lft-out--
449×cbrt-prod
260×associate-*l/
178×swap-sqr
168×cbrt-div
126×frac-sub
124×distribute-lft-out
107×add-sqr-sqrt
84×tan-quot flip3-- flip--
64×frac-times
42×flip3-+ frac-add flip-+
32×unswap-sqr
28×difference-of-squares
22×associate-*r*
15×add-cube-cbrt
11×pow1
9×pow1/3
8×associate-*r/ add-cbrt-cube
6×add-exp-log
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative
Counts
4 → 440
Calls
4 calls:
86.0ms
(* (cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))) (cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))))
32.0ms
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))
34.0ms
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))
32.0ms
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))

series2.0s

Counts
4 → 12
Calls
4 calls:
540.0ms
(* (cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))) (cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a)))))
482.0ms
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))
481.0ms
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))
486.0ms
(cbrt (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))))

simplify227.0ms

Algorithm
egg-herbie
Counts
452 → 452
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
075717848
1294216996
2500114586

prune1.3s

Filtered
452 candidates to 160 candidates (35.4%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New4520452
Fresh066
Picked011
Done022
Total4529461

Merged error: 0.0b

Counts
461 → 9

regimes657.0ms

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 (1.0ms)

IterNodesCost
02620
12620

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.7s3841×body1280valid
472.0ms1974×body640valid
324.0ms8000×pre80true
104.0ms655×body320valid
58.0ms1223×body80valid
34.0ms307×body160valid