Details

Time bar (total: 1.7m)

sample478.0ms

Algorithm
intervals
Results
263.0ms122×body1280valid
108.0ms68×body640valid
31.0ms256×pre80true
19.0ms23×body320valid
9.0ms32×body80valid
7.0ms11×body160valid

simplify85.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
85.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite64.0ms

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
28.0ms
(- (tan (+ y z)) (tan a))
23.0ms
(+ x (- (tan (+ y z)) (tan a)))
11.0ms
(tan (+ y z))

series461.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
178.0ms
(- (tan (+ y z)) (tan a))
176.0ms
(+ x (- (tan (+ y z)) (tan a)))
106.0ms
(tan (+ y z))

simplify3.8s

Counts
56 → 84
Calls
56 calls:
Slowest
301.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
207.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
186.0ms
(fma 1 (tan (+ y z)) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
181.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
179.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite260.0ms

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
144.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
82.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms
(* (tan y) (tan z))
15.0ms
(+ (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
587.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
545.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
147.0ms
(* (tan y) (tan z))
131.0ms
(+ (tan y) (tan z))

simplify26.4s

Counts
228 → 223
Calls
228 calls:
Slowest
576.0ms
(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)))))
523.0ms
(* (cbrt (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (cbrt (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))
520.0ms
(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)))))
472.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
459.0ms
(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

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (tan y) (tan z)) 3)
0.3b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.2b
(* (tan y) (tan z))
0.2b
(* (tan y) (tan z))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
50×pow1
44×tan-quot
23×add-cbrt-cube add-exp-log
20×frac-times pow-prod-down
14×associate-*l/ associate-*r/
13×add-sqr-sqrt
11×prod-exp cbrt-unprod
9×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
4×expm1-log1p-u pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×cube-div pow-unpow *-commutative
2×pow-pow pow-plus pow-exp rem-cube-cbrt unswap-sqr
1×pow2 cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod swap-sqr sqr-pow
Counts
4 → 128
Calls
4 calls:
Slowest
133.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
22.0ms
(pow (* (tan y) (tan z)) 3)
15.0ms
(* (tan y) (tan z))
14.0ms
(* (tan y) (tan z))

series637.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(pow (* (tan y) (tan z)) 3)
179.0ms
(* (tan y) (tan z))
155.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
117.0ms
(* (tan y) (tan z))

simplify8.8s

Counts
111 → 140
Calls
111 calls:
Slowest
1.2s
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
1.1s
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
882.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
815.0ms
(* (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
363.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune3.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize132.0ms

Local error

Found 4 expressions with local error:

7.9b
(cbrt (* (* (pow (* (tan y) (tan z)) 3) (pow (* (tan y) (tan z)) 3)) (pow (* (tan y) (tan z)) 3)))
0.3b
(pow (* (tan y) (tan z)) 3)
0.3b
(pow (* (tan y) (tan z)) 3)
0.3b
(pow (* (tan y) (tan z)) 3)

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
204×tan-quot
153×cube-div
132×frac-times
78×associate-*l/
66×associate-*r/
63×cbrt-div
13×pow1 add-cbrt-cube add-exp-log
9×pow-unpow
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-pow pow-exp rem-cube-cbrt
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod prod-exp cbrt-unprod sqr-pow
2×rem-cbrt-cube
1×cbrt-prod pow1/3 pow3
Counts
4 → 161
Calls
4 calls:
Slowest
110.0ms
(cbrt (* (* (pow (* (tan y) (tan z)) 3) (pow (* (tan y) (tan z)) 3)) (pow (* (tan y) (tan z)) 3)))
11.0ms
(pow (* (tan y) (tan z)) 3)
11.0ms
(pow (* (tan y) (tan z)) 3)
11.0ms
(pow (* (tan y) (tan z)) 3)

series692.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(pow (* (tan y) (tan z)) 3)
177.0ms
(cbrt (* (* (pow (* (tan y) (tan z)) 3) (pow (* (tan y) (tan z)) 3)) (pow (* (tan y) (tan z)) 3)))
168.0ms
(pow (* (tan y) (tan z)) 3)
164.0ms
(pow (* (tan y) (tan z)) 3)

simplify35.5s

Counts
117 → 173
Calls
117 calls:
Slowest
1.1s
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
999.0ms
(cbrt (* (* (pow (* (tan y) (sin z)) 3) (pow (* (sin y) (tan z)) 3)) (pow (* (sin y) (sin z)) 3)))
771.0ms
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
770.0ms
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
770.0ms
(cbrt (* (pow (* (tan y) (tan z)) 3) (pow (* (tan y) (tan z)) 3)))

prune3.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes412.0ms

Accuracy

0% (0.1b remaining)

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

bsearch10.0ms

end0.0ms

sample12.1s

Algorithm
intervals
Results
7.7s3904×body1280valid
2.5s1955×body640valid
681.0ms8000×pre80true
475.0ms722×body320valid
299.0ms1147×body80valid
110.0ms272×body160valid