Details

Time bar (total: 1.1m)

sample388.0ms

Algorithm
intervals
Results
182.0ms106×body1280valid
82.0ms71×body640valid
63.0ms21×body2560valid
39.0ms17×body320valid
7.0ms31×body80valid
4.0ms10×body160valid

simplify9.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
9.0ms
(- (tan (+ x eps)) (tan x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize50.0ms

Local error

Found 2 expressions with local error:

2.8b
(tan (+ x eps))
1.1b
(- (tan (+ x eps)) (tan x))

rewrite37.0ms

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
26.0ms
(- (tan (+ x eps)) (tan x))
11.0ms
(tan (+ x eps))

series188.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
117.0ms
(- (tan (+ x eps)) (tan x))
70.0ms
(tan (+ x eps))

simplify2.8s

Counts
35 → 49
Calls
35 calls:
Slowest
506.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
252.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
222.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
195.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
171.0ms
(fma 1 (tan (+ x eps)) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune559.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.1b

localize36.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))

rewrite182.0ms

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
97.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
48.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
17.0ms
(+ (tan x) (tan eps))
16.0ms
(* (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
564.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
297.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
143.0ms
(* (tan x) (tan eps))
136.0ms
(+ (tan x) (tan eps))

simplify24.0s

Counts
201 → 185
Calls
201 calls:
Slowest
714.0ms
(fma (/ 1 (sqrt (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
511.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) 1) (/ (sqrt (+ (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
481.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
467.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
454.0ms
(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))))))

prune2.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.0b

localize37.0ms

Local error

Found 4 expressions with local error:

3.1b
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
0.2b
(* (tan x) (tan eps))
0.1b
(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
15×add-cube-cbrt
10×add-exp-log
9×times-frac
8×add-cbrt-cube
7×pow1
6×tan-quot add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def associate-*r* associate-*l* associate-/l*
2×div-exp associate-/r/
1×frac-times cbrt-undiv +-commutative rec-exp clear-num sum-log frac-2neg flip3-+ flip3-- 1-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ fma-udef div-inv pow-flip flip-- distribute-lft-out inv-pow unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
15.0ms
(+ (tan x) (tan eps))
15.0ms
(* (tan x) (tan eps))
9.0ms
(/ 1 (- 1 (* (tan x) (tan eps))))
0.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series838.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
435.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
174.0ms
(/ 1 (- 1 (* (tan x) (tan eps))))
128.0ms
(+ (tan x) (tan eps))
100.0ms
(* (tan x) (tan eps))

simplify4.4s

Counts
61 → 102
Calls
61 calls:
Slowest
535.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
358.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* x eps) 1))
333.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))
330.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
306.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.0b

localize74.0ms

Local error

Found 4 expressions with local error:

3.1b
(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.2b
(* (tan eps) (tan x))

rewrite191.0ms

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×prod-exp cbrt-unprod
8×add-sqr-sqrt pow-sqr pow-prod-up
6×*-un-lft-identity add-cube-cbrt
5×associate-*r* associate-*l*
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow2 swap-sqr
1×fma-udef unswap-sqr
Counts
4 → 139
Calls
4 calls:
Slowest
89.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
84.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
15.0ms
(* (tan eps) (tan x))
0.0ms
(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
145.0ms
(* (tan eps) (tan x))
141.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
140.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))

simplify9.7s

Counts
142 → 151
Calls
142 calls:
Slowest
982.0ms
(* (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))))
883.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
729.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
696.0ms
(* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))) (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))
564.0ms
(- (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))) (+ (/ (* (pow (sin x) 3) (pow (sin eps) 2)) (* (pow (cos x) 3) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))) (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (pow (cos eps) 3) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))) (+ (/ (sin eps) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos eps))) (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))))))) (/ (sin x) (cos x)))

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.0b

regimes221.0ms

Accuracy

60.2% (2.9b remaining)

Error of 15.3b against oracle of 12.4b and baseline of 19.6b

bsearch1.2s

end0.0ms

sample12.8s

Algorithm
intervals
Results
5.8s3236×body1280valid
3.1s1967×body640valid
2.1s616×body2560valid
940.0ms1070×body80valid
601.0ms767×body320valid
158.0ms344×body160valid