Details

Time bar (total: 22.2s)

sample282.0ms

Algorithm
intervals
Results
184.0ms128×body1280valid
35.0ms59×body640valid
13.0ms256×pre80true
8.0ms16×body320valid
5.0ms40×body80valid
4.0ms13×body160valid

simplify109.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b
(+ x (- (tan (+ y z)) (tan a)))
0.2b
(- (tan (+ y z)) (tan a))
2.7b
(tan (+ y z))

rewrite63.0ms

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:
36.0ms
(+ x (- (tan (+ y z)) (tan a)))
18.0ms
(- (tan (+ y z)) (tan a))
7.0ms
(tan (+ y z))

series418.0ms

Counts
3 → 9
Calls
3 calls:
181.0ms
(+ x (- (tan (+ y z)) (tan a)))
180.0ms
(- (tan (+ y z)) (tan a))
57.0ms
(tan (+ y z))

simplify651.0ms

Counts
51 → 51

prune198.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite433.0ms

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:
60.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
193.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
150.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
26.0ms
(* (tan y) (tan z))

series1.6s

Counts
4 → 12
Calls
4 calls:
298.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
623.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
584.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
117.0ms
(* (tan y) (tan z))

simplify785.0ms

Counts
102 → 102

prune466.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ 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))
0.2b
(* (tan y) (tan z))
2.1b
(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite835.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
17×add-log-exp
14×add-sqr-sqrt
7×add-cube-cbrt
6×pow1 add-exp-log add-cbrt-cube
5×tan-quot exp-prod
4×sum-log distribute-lft-out
3×diff-log associate-*r* associate-*l* rem-exp-log distribute-lft-out--
2×associate-+r- sub-neg associate-+r+ difference-of-squares
1×+-commutative frac-times flip3-- flip3-+ times-frac exp-diff associate-*r/ exp-sum pow-prod-down associate-*l/ prod-exp *-commutative frac-sub flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 71
Calls
4 calls:
146.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
97.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
19.0ms
(* (tan y) (tan z))
570.0ms
(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.9s

Counts
4 → 12
Calls
4 calls:
487.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
620.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
162.0ms
(* (tan y) (tan z))
592.0ms
(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify1.3s

Counts
83 → 83

prune404.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite374.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
13×tan-quot
12×*-un-lft-identity
10×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
9×associate-*r* associate-*l*
6×times-frac add-log-exp
5×difference-of-squares
3×frac-times associate-*r/ pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
2×cbrt-prod
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out--
Counts
4 → 82
Calls
4 calls:
294.0ms
(- (/ (/ (+ (tan y) (tan z)) (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (cbrt (- 1 (* (tan y) (tan z))))) (tan a))
26.0ms
(* (tan y) (tan z))
25.0ms
(* (tan y) (tan z))
25.0ms
(* (tan y) (tan z))

series911.0ms

Counts
4 → 12
Calls
4 calls:
569.0ms
(- (/ (/ (+ (tan y) (tan z)) (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (cbrt (- 1 (* (tan y) (tan z))))) (tan a))
128.0ms
(* (tan y) (tan z))
106.0ms
(* (tan y) (tan z))
108.0ms
(* (tan y) (tan z))

simplify946.0ms

Counts
94 → 94

prune591.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes417.0ms

Accuracy

-1.8% (0.2b remaining)

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

bsearch0.0ms

simplify684.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
4.8s3884×body1280valid
1.7s1944×body640valid
732.0ms8000×pre80true
547.0ms1197×body80valid
350.0ms669×body320valid
124.0ms306×body160valid