Details

Time bar (total: 1.3m)

sample487.0ms

Algorithm
intervals
Results
222.0ms113×body1280valid
154.0ms77×body640valid
29.0ms256×pre80true
17.0ms17×body320valid
10.0ms10×body160valid
10.0ms39×body80valid

simplify80.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
80.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize33.0ms

Local error

Found 3 expressions with local error:

4.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
2×tan-sum associate-+r+ 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 → 45
Calls
3 calls:
Slowest
19.0ms
(+ x (- (tan (+ y z)) (tan a)))
12.0ms
(- (tan (+ y z)) (tan a))
4.0ms
(tan (+ y z))

series387.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
165.0ms
(- (tan (+ y z)) (tan a))
148.0ms
(+ x (- (tan (+ y z)) (tan a)))
73.0ms
(tan (+ y z))

simplify1.6s

Counts
25 → 54
Calls
25 calls:
Slowest
470.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
176.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
162.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
128.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))
123.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))

prune623.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite284.0ms

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-cbrt-cube add-exp-log
7×tan-quot
6×pow1 distribute-lft-out
4×insert-posit16 associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×associate-+r+ sum-log sub-neg flip3-+ flip3-- diff-log associate-/r/ flip-+ flip-- distribute-lft-out-- difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num associate-+r- frac-2neg div-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod div-inv unswap-sqr
Counts
4 → 94
Calls
4 calls:
Slowest
134.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
92.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
33.0ms
(* (tan y) (tan z))
24.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
514.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
510.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
287.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
130.0ms
(* (tan y) (tan z))

simplify6.2s

Counts
77 → 106
Calls
77 calls:
Slowest
567.0ms
(/ (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))))
413.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
342.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
331.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
329.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

3.6b
(log (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))
0.4b
(exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
0.2b
(* (tan y) (tan z))
0.2b
(- (log (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (tan a))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
36×exp-prod
28×add-sqr-sqrt
24×times-frac add-cube-cbrt
20×log-pow
8×pow1
6×log-prod add-cbrt-cube add-exp-log distribute-lft-out add-log-exp
4×tan-quot associate-/r/ insert-posit16
3×flip3-- associate-*r* associate-*l* associate--l+ flip--
2×div-inv distribute-lft-out--
1×frac-times sub-neg diff-log rem-log-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
Counts
4 → 99
Calls
4 calls:
Slowest
185.0ms
(- (log (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (tan a))
38.0ms
(exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
35.0ms
(log (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))
13.0ms
(* (tan y) (tan z))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
537.0ms
(- (log (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (tan a))
286.0ms
(log (exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))
273.0ms
(exp (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
121.0ms
(* (tan y) (tan z))

simplify5.0s

Counts
75 → 111
Calls
75 calls:
Slowest
347.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
286.0ms
(/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))
283.0ms
(exp (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))
278.0ms
(exp (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))
267.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))) (/ (sin a) (cos a)))

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

29.6b
(cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
3.6b
(log (exp (/ (+ (tan y) (tan z)) (- 1 (cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))))))
0.4b
(exp (/ (+ (tan y) (tan z)) (- 1 (cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z)))))))
0.3b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
224×tan-quot
146×frac-times
86×associate-*l/
75×*-un-lft-identity
74×associate-*r/
63×cbrt-div
60×exp-prod
51×add-sqr-sqrt
48×times-frac
44×pow1
31×log-pow
27×add-cube-cbrt
17×pow-prod-down
16×add-cbrt-cube add-exp-log difference-of-squares
12×distribute-lft-out
8×prod-exp cbrt-unprod distribute-lft-out--
5×add-log-exp
4×associate-/r/ pow-sqr pow-prod-up insert-posit16
3×log-prod
2×pow-plus flip3-- div-inv flip--
1×cbrt-prod pow2 pow1/3 swap-sqr rem-log-exp associate-*r* associate-*l* pow3 *-commutative rem-cbrt-cube rem-exp-log
Counts
4 → 206
Calls
4 calls:
Slowest
170.0ms
(cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
76.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
34.0ms
(log (exp (/ (+ (tan y) (tan z)) (- 1 (cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))))))
23.0ms
(exp (/ (+ (tan y) (tan z)) (- 1 (cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z)))))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
288.0ms
(log (exp (/ (+ (tan y) (tan z)) (- 1 (cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))))))
288.0ms
(exp (/ (+ (tan y) (tan z)) (- 1 (cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z)))))))
126.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
111.0ms
(cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))

simplify40.2s

Counts
200 → 218
Calls
200 calls:
Slowest
856.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
742.0ms
(exp (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) (+ 1 (sqrt (cbrt (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))))))
663.0ms
(* (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
475.0ms
(cbrt (* (* (* (tan y) (sin z)) (* (sin y) (tan z))) (* (sin y) (tan z))))
469.0ms
(cbrt (* (* (* (sin y) (tan z)) (* (sin y) (sin z))) (* (tan y) (tan z))))

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes368.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample12.8s

Algorithm
intervals
Results
7.5s3857×body1280valid
3.3s1983×body640valid
785.0ms8000×pre80true
490.0ms700×body320valid
300.0ms1201×body80valid
206.0ms259×body160valid