Details

Time bar (total: 1.2m)

sample543.0ms

Algorithm
intervals
Results
264.0ms124×body1280valid
124.0ms57×body640valid
61.0ms51×body80valid
35.0ms256×pre80true
19.0ms21×body320valid
2.0ms3×body160valid

simplify72.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
72.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize25.0ms

Local error

Found 3 expressions with local error:

2.8b
(tan (+ y z))
0.1b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite43.0ms

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×expm1-log1p-u pow1 fma-def add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×tan-sum sum-log sub-neg diff-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-+ flip3-- flip-+ flip-- difference-of-squares
Counts
3 → 75
Calls
3 calls:
Slowest
19.0ms
(- (tan (+ y z)) (tan a))
17.0ms
(+ x (- (tan (+ y z)) (tan a)))
6.0ms
(tan (+ y z))

series503.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
211.0ms
(- (tan (+ y z)) (tan a))
204.0ms
(+ x (- (tan (+ y z)) (tan a)))
87.0ms
(tan (+ y z))

simplify3.5s

Counts
56 → 84
Calls
56 calls:
Slowest
308.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
205.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
194.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
177.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))
175.0ms
(+ (* 1/3 (pow y 3)) (+ z y))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite335.0ms

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 fma-def add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×sum-log associate-*r* associate-*l*
2×+-commutative sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 211
Calls
4 calls:
Slowest
175.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
122.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
23.0ms
(* (tan y) (tan z))
8.0ms
(+ (tan y) (tan z))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
650.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
578.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
158.0ms
(* (tan y) (tan z))
121.0ms
(+ (tan y) (tan z))

simplify26.2s

Counts
228 → 223
Calls
228 calls:
Slowest
732.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))
573.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
555.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
505.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
455.0ms
(fma (/ 1 (sqrt (- 1 (* (tan y) (tan z))))) (/ (+ (tan y) (tan z)) (sqrt (- 1 (* (tan y) (tan z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune3.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
0.3b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.2b
(* (tan y) (tan z))
0.2b
(* (tan y) (tan z))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
72×tan-quot
36×frac-times pow-prod-down
32×add-cbrt-cube add-exp-log
24×associate-*l/ associate-*r/
18×prod-exp cbrt-unprod
12×add-sqr-sqrt
8×*-un-lft-identity associate-*r* associate-*l* pow-sqr pow-prod-up add-cube-cbrt
4×expm1-log1p-u pow-plus *-commutative insert-posit16 log1p-expm1-u add-log-exp
2×pow2 swap-sqr unswap-sqr
Counts
4 → 152
Calls
4 calls:
Slowest
112.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
86.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
32.0ms
(* (tan y) (tan z))
30.0ms
(* (tan y) (tan z))

series731.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
214.0ms
(* (* (tan z) (tan y)) (* (tan z) (tan y)))
193.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
169.0ms
(* (tan y) (tan z))
154.0ms
(* (tan y) (tan z))

simplify9.2s

Counts
156 → 164
Calls
156 calls:
Slowest
993.0ms
(* (* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y))) (* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y))))
854.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
776.0ms
(* (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
667.0ms
(* (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))) (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))
344.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune3.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize131.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (* (tan y) (tan z)))
5.5b
(cbrt (* (tan y) (tan z)))
5.5b
(cbrt (* (tan y) (tan z)))
0.5b
(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
44×tan-quot
33×cbrt-div
20×frac-times
14×associate-*l/ associate-*r/
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×*-un-lft-identity add-cube-cbrt
7×cbrt-prod
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube swap-sqr associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 94
Calls
4 calls:
Slowest
75.0ms
(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
17.0ms
(cbrt (* (tan y) (tan z)))
15.0ms
(cbrt (* (tan y) (tan z)))
10.0ms
(cbrt (* (tan y) (tan z)))

series890.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
241.0ms
(cbrt (* (tan y) (tan z)))
235.0ms
(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
208.0ms
(cbrt (* (tan y) (tan z)))
206.0ms
(cbrt (* (tan y) (tan z)))

simplify3.8s

Counts
78 → 106
Calls
78 calls:
Slowest
347.0ms
(+ (exp (* 1/3 (+ (* 2 (log z)) (* 2 (log y))))) (+ (* 2/9 (* (exp (* 1/3 (+ (* 2 (log z)) (* 2 (log y))))) (pow z 2))) (* 2/9 (* (exp (* 1/3 (+ (* 2 (log z)) (* 2 (log y))))) (pow y 2)))))
337.0ms
(pow (/ (* (sin z) (sin y)) (* (cos y) (cos z))) 1/3)
287.0ms
(pow (/ (* (sin z) (sin y)) (* (cos y) (cos z))) 1/3)
285.0ms
(pow (/ (* (sin z) (sin y)) (* (cos y) (cos z))) 1/3)
279.0ms
(pow (/ (* (sin z) (sin y)) (* (cos y) (cos z))) 1/3)

prune2.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes510.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample15.0s

Algorithm
intervals
Results
9.3s3903×body1280valid
2.6s1954×body640valid
1.6s8000×pre80true
600.0ms729×body320valid
371.0ms1124×body80valid
187.0ms290×body160valid