Details

Time bar (total: 36.6s)

sample325.0ms

Algorithm
intervals
Results
165.0ms112×body1280valid
69.0ms77×body640valid
19.0ms256×pre80true
8.0ms43×body80valid
8.0ms13×body320valid
4.0ms11×body160valid

simplify7.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
1159
2229
3339
4399
5899
61939
74519
813809
948379
done50019

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))
3.9b
(tan (+ y z))

rewrite62.0ms

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×pow1 add-exp-log expm1-log1p-u fma-def fma-neg add-cbrt-cube log1p-expm1-u
2×sub-neg tan-sum 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 → 72
Calls
3 calls:
19.0ms
(+ x (- (tan (+ y z)) (tan a)))
26.0ms
(- (tan (+ y z)) (tan a))
13.0ms
(tan (+ y z))

series418.0ms

Counts
3 → 9
Calls
3 calls:
183.0ms
(+ x (- (tan (+ y z)) (tan a)))
163.0ms
(- (tan (+ y z)) (tan a))
72.0ms
(tan (+ y z))

simplify895.0ms

Counts
81 → 81
Iterations

Useful iterations: done (891.0ms)

IterNodesCost
01281195
12831011
21003882
done5000795

prune388.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite470.0ms

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 add-exp-log fma-def add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* associate-*l* sum-log
2×+-commutative sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- associate-*r/ pow-prod-down associate-*l/ frac-add prod-exp *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 207
Calls
4 calls:
18.0ms
(+ (tan y) (tan z))
198.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
213.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
18.0ms
(* (tan y) (tan z))

series1.6s

Counts
4 → 12
Calls
4 calls:
141.0ms
(+ (tan y) (tan z))
696.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
607.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
150.0ms
(* (tan y) (tan z))

simplify3.2s

Counts
219 → 219
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02966641
17015567
226965029
done50014409

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b
(* (tan y) (tan z))
2.5b
(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
154×*-un-lft-identity
108×prod-diff
107×add-sqr-sqrt
100×add-cube-cbrt
85×times-frac
56×associate-+r+
25×distribute-lft-out
18×fma-neg
17×add-log-exp
14×associate-/r/
8×flip3-- flip--
7×div-inv
6×pow1 add-exp-log add-cbrt-cube
5×tan-quot exp-prod
4×expm1-log1p-u sum-log log1p-expm1-u
3×fma-def diff-log associate-*r* associate-*l* rem-exp-log distribute-lft-out--
2×associate-+r- sub-neg difference-of-squares
1×+-commutative frac-times flip3-+ exp-diff associate-*r/ exp-sum pow-prod-down associate-*l/ prod-exp *-commutative frac-sub cbrt-unprod flip-+ unswap-sqr
Counts
4 → 208
Calls
4 calls:
148.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
227.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
19.0ms
(* (tan y) (tan z))
729.0ms
(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series2.1s

Counts
4 → 12
Calls
4 calls:
571.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
563.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
152.0ms
(* (tan y) (tan z))
819.0ms
(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify2.0s

Counts
220 → 220
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02886913
16675850
225975275
done50014655

prune821.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite360.0ms

Algorithm
rewrite-expression-head
Rules
235×times-frac
181×add-sqr-sqrt *-un-lft-identity
180×prod-diff
174×add-cube-cbrt
92×associate-+r+
36×associate-/r/
30×fma-neg
29×div-inv
22×cos-mult
11×add-exp-log add-cbrt-cube add-log-exp
8×flip3-- flip--
6×pow1
5×tan-quot
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l* associate-/l*
2×cbrt-undiv sub-neg diff-log div-exp prod-exp sum-log cbrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative frac-times associate-+r- frac-2neg flip3-+ associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative frac-sub flip-+ unswap-sqr
Counts
4 → 297
Calls
4 calls:
118.0ms
(- (/ (/ (fma (sin y) (cos z) (* (cos y) (sin z))) (* (cos z) (cos y))) (- 1 (* (tan y) (tan z)))) (tan a))
193.0ms
(+ x (- (/ (/ (fma (sin y) (cos z) (* (cos y) (sin z))) (* (cos z) (cos y))) (- 1 (* (tan y) (tan z)))) (tan a)))
16.0ms
(* (tan y) (tan z))
10.0ms
(/ (fma (sin y) (cos z) (* (cos y) (sin z))) (* (cos z) (cos y)))

series1.1s

Counts
4 → 12
Calls
4 calls:
432.0ms
(- (/ (/ (fma (sin y) (cos z) (* (cos y) (sin z))) (* (cos z) (cos y))) (- 1 (* (tan y) (tan z)))) (tan a))
392.0ms
(+ x (- (/ (/ (fma (sin y) (cos z) (* (cos y) (sin z))) (* (cos z) (cos y))) (- 1 (* (tan y) (tan z)))) (tan a)))
110.0ms
(* (tan y) (tan z))
176.0ms
(/ (fma (sin y) (cos z) (* (cos y) (sin z))) (* (cos z) (cos y)))

simplify1.7s

Counts
309 → 309
Iterations

Useful iterations: 2 (595.0ms)

IterNodesCost
044614184
1102312464
2415411532
done500011532

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes311.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02855
13655
done3655

end0.0ms

sample9.5s

Algorithm
intervals
Results
4.5s3829×body1280valid
2.4s2050×body640valid
680.0ms691×body320valid
642.0ms1130×body80valid
574.0ms8000×pre80true
85.0ms300×body160valid