Details

Time bar (total: 2.0m)

sample397.0ms

Algorithm
intervals
Results
225.0ms107×body1280valid
64.0ms60×body640valid
58.0ms18×body2560valid
21.0ms29×body320valid
9.0ms16×body160valid
6.0ms26×body80valid

simplify17.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize14.0ms

Local error

Found 2 expressions with local error:

3.0b
(tan (+ x eps))
1.5b
(- (tan (+ x eps)) (tan x))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×tan-quot add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 tan-sum add-cbrt-cube add-exp-log frac-sub insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
Slowest
31.0ms
(tan (+ x eps))
30.0ms
(- (tan (+ x eps)) (tan x))

series169.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
108.0ms
(- (tan (+ x eps)) (tan x))
60.0ms
(tan (+ x eps))

simplify4.2s

Counts
65 → 49
Calls
65 calls:
Slowest
567.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
377.0ms
(* (* (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x))) (- (tan (+ x eps)) (tan x)))
267.0ms
(- (pow (tan (+ x eps)) 3) (pow (tan x) 3))
240.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
234.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))

prune482.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize30.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.3b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
73×add-sqr-sqrt
66×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1 flip3-- flip--
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* fma-def associate-*r* associate-*l* associate-/l/
2×flip3-+ frac-add flip-+ difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 173
Calls
4 calls:
Slowest
96.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
49.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
28.0ms
(* (tan x) (tan eps))
16.0ms
(+ (tan x) (tan eps))

series997.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
442.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
310.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
124.0ms
(+ (tan x) (tan eps))
121.0ms
(* (tan x) (tan eps))

simplify29.2s

Counts
257 → 185
Calls
257 calls:
Slowest
700.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
646.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
626.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
556.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (/ (sqrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
524.0ms
(* (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))))

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.9b

localize75.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (tan x) (tan eps))

rewrite312.0ms

Algorithm
rewrite-expression-head
Rules
130×*-un-lft-identity
95×add-sqr-sqrt
84×pow1
81×times-frac
78×prod-diff
72×add-cube-cbrt
69×tan-quot
35×frac-times pow-prod-down
34×difference-of-squares
30×add-cbrt-cube add-exp-log
26×fma-neg
23×associate-*l/ associate-*r/
20×distribute-lft-out
17×prod-exp cbrt-unprod
8×associate-/r/ pow-sqr pow-prod-up
6×add-log-exp
5×flip3-- associate-*r* associate-*l* flip--
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u div-inv
3×*-commutative
2×pow2 swap-sqr
1×sub-neg diff-log frac-sub distribute-lft-out-- unswap-sqr
Counts
4 → 251
Calls
4 calls:
Slowest
106.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
96.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
72.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
29.0ms
(* (tan x) (tan eps))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
669.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
191.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
172.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
121.0ms
(* (tan x) (tan eps))

simplify40.8s

Counts
363 → 263
Calls
363 calls:
Slowest
735.0ms
(fma (/ 1 (+ 1 (* (tan x) (tan eps)))) (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (- (* (tan x) 1)))
679.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
584.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
538.0ms
(fma (/ (* (cbrt (+ (tan eps) (tan x))) (cbrt (+ (tan eps) (tan x)))) (* (cbrt (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (cbrt (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))) (/ (cbrt (+ (tan eps) (tan x))) (cbrt (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (* (tan x) 1)))
537.0ms
(fma (/ (* (cbrt (+ (tan eps) (tan x))) (cbrt (+ (tan eps) (tan x)))) 1) (/ (cbrt (+ (tan eps) (tan x))) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (- (* (tan x) 1)))

prune2.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

3.5b
(log (exp (* (tan x) (tan eps))))
2.3b
(- (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (log (exp (* (tan x) (tan eps))))))) (tan x))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (tan x) (tan eps))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
64×add-sqr-sqrt
57×add-cube-cbrt
54×prod-diff
49×times-frac
46×pow1
37×tan-quot
18×frac-times add-cbrt-cube fma-neg pow-prod-down add-exp-log
12×associate-*l/ associate-*r/ distribute-lft-out
9×prod-exp cbrt-unprod
8×associate-/r/
7×add-log-exp
5×flip3-- flip--
4×expm1-log1p-u associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 log1p-expm1-u div-inv
3×log-prod log-pow
2×pow-plus *-commutative difference-of-squares
1×pow2 exp-prod sub-neg exp-to-pow diff-log swap-sqr rem-log-exp frac-sub distribute-lft-out-- unswap-sqr
Counts
4 → 184
Calls
4 calls:
Slowest
62.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
61.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (log (exp (* (tan x) (tan eps))))))) (tan x))
14.0ms
(* (tan x) (tan eps))
4.0ms
(log (exp (* (tan x) (tan eps))))

series789.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
500.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (log (exp (* (tan x) (tan eps))))))) (tan x))
107.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
93.0ms
(log (exp (* (tan x) (tan eps))))
90.0ms
(* (tan x) (tan eps))

simplify24.6s

Counts
266 → 196
Calls
266 calls:
Slowest
568.0ms
(fma (sqrt (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (log (exp (* (tan x) (tan eps)))))))) (sqrt (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (log (exp (* (tan x) (tan eps)))))))) (- (* (tan x) 1)))
561.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
469.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
453.0ms
(* (- 1 (* (* (tan x) (tan eps)) (log (exp (* (tan x) (tan eps)))))) (cos x))
349.0ms
(fma 1 (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan x) (tan eps)) (log (exp (* (tan x) (tan eps))))))) (- (* (tan x) 1)))

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

regimes177.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 20.3b

bsearch274.0ms

end0.0ms

sample10.2s

Algorithm
intervals
Results
5.4s3192×body1280valid
1.9s1804×body640valid
1.8s689×body2560valid
485.0ms820×body320valid
233.0ms1138×body80valid
153.0ms357×body160valid