Details

Time bar (total: 1.9m)

sample452.0ms

Algorithm
intervals
Results
207.0ms105×body1280valid
102.0ms64×body640valid
94.0ms18×body2560valid
18.0ms20×body320valid
10.0ms39×body80valid
7.0ms10×body160valid

simplify16.0ms

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: 35.3b

localize28.0ms

Local error

Found 2 expressions with local error:

4.0b
(tan (+ x eps))
0.6b
(- (tan (+ x eps)) (tan x))

rewrite27.0ms

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
16.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series225.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
156.0ms
(- (tan (+ x eps)) (tan x))
70.0ms
(tan (+ x eps))

simplify2.7s

Counts
35 → 49
Calls
35 calls:
Slowest
477.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
235.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
196.0ms
(fma (* (cbrt (tan (+ x eps))) (cbrt (tan (+ x eps)))) (cbrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
191.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
183.0ms
(fma 1 (tan (+ x eps)) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune523.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.9b

localize26.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.3b
(* (tan x) (tan eps))
0.2b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite150.0ms

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
80.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
35.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms
(* (tan x) (tan eps))
8.0ms
(+ (tan x) (tan eps))

series966.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
458.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
274.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
129.0ms
(+ (tan x) (tan eps))
105.0ms
(* (tan x) (tan eps))

simplify23.9s

Counts
201 → 185
Calls
201 calls:
Slowest
909.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
492.0ms
(fma (sqrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (sqrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
481.0ms
(fma (* (cbrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (cbrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))))) (cbrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
461.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
451.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (+ (tan x) (tan eps)) (cbrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune1.9s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.7b

localize63.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 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))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
68×tan-quot
35×frac-times pow-prod-down
30×add-cbrt-cube add-exp-log
23×associate-*l/ associate-*r/
17×add-sqr-sqrt prod-exp cbrt-unprod
15×*-un-lft-identity
13×add-cube-cbrt
9×prod-diff
8×pow-sqr pow-prod-up
6×add-log-exp
5×associate-*r* associate-*l*
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u
3×fma-neg *-commutative
2×pow2 swap-sqr
1×sub-neg flip3-- diff-log associate--l+ fma-udef flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 158
Calls
4 calls:
Slowest
108.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
94.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
27.0ms
(* (tan x) (tan eps))
10.0ms
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
945.0ms
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x))
155.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
154.0ms
(* (tan x) (tan eps))
151.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))

simplify15.7s

Counts
167 → 170
Calls
167 calls:
Slowest
976.0ms
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (/ (sin eps) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))))) (/ (sin x) (cos x)))
897.0ms
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (/ (sin eps) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))))) (/ (sin x) (cos x)))
874.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
859.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
760.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

prune2.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.7b

localize68.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b
(* (tan eps) (tan x))

rewrite337.0ms

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
100.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))
99.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
99.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
29.0ms
(* (tan eps) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
637.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))
185.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
143.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
121.0ms
(* (tan eps) (tan x))

simplify42.8s

Counts
331 → 263
Calls
331 calls:
Slowest
855.0ms
(* (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))))
805.0ms
(* (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))))
729.0ms
(* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))) (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))
706.0ms
(fma (/ (* (cbrt (+ (tan x) (tan eps))) (cbrt (+ (tan x) (tan eps)))) (sqrt (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (/ (cbrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (- (* (tan x) 1)))
667.0ms
(* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))) (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))

prune3.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.0b

regimes284.0ms

Accuracy

75.8% (2.2b remaining)

Error of 12.0b against oracle of 9.8b and baseline of 19.0b

bsearch446.0ms

end0.0ms

sample13.0s

Algorithm
intervals
Results
6.8s3338×body1280valid
3.0s1806×body640valid
2.0s606×body2560valid
586.0ms763×body320valid
268.0ms1124×body80valid
207.0ms363×body160valid