Details

Time bar (total: 57.1s)

sample479.0ms

Algorithm
intervals
Results
239.0ms100×body1280valid
89.0ms71×body640valid
62.0ms17×body2560valid
39.0ms12×body160valid
29.0ms29×body320valid
7.0ms27×body80valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(- (tan (+ x eps)) (tan x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize13.0ms

Local error

Found 2 expressions with local error:

3.0b
(tan (+ x eps))
2.4b
(- (tan (+ x eps)) (tan x))

rewrite36.0ms

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
29.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series218.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
128.0ms
(- (tan (+ x eps)) (tan x))
90.0ms
(tan (+ x eps))

simplify2.8s

Counts
35 → 49
Calls
35 calls:
Slowest
476.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
257.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
205.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
201.0ms
(fma (* (cbrt (tan (+ x eps))) (cbrt (tan (+ x eps)))) (cbrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
180.0ms
(fma 1 (tan (+ x eps)) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune553.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.6b

localize30.0ms

Local error

Found 4 expressions with local error:

4.3b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite177.0ms

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
106.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
34.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
24.0ms
(* (tan x) (tan eps))
8.0ms
(+ (tan x) (tan eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
502.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
271.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
139.0ms
(+ (tan x) (tan eps))
120.0ms
(* (tan x) (tan eps))

simplify23.8s

Counts
201 → 185
Calls
201 calls:
Slowest
833.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (sqrt (+ (tan x) (tan eps))) (cbrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
552.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
512.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
505.0ms
(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))))))
442.0ms
(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))))))

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.5b

localize33.0ms

Local error

Found 4 expressions with local error:

4.3b
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
0.2b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(- 1 (* (tan x) (tan eps)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt
8×add-log-exp
6×pow1 add-cbrt-cube tan-quot add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def fma-neg associate-*r* associate-*l* prod-diff
1×frac-times +-commutative sum-log sub-neg flip3-+ flip3-- diff-log pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ fma-udef flip-- distribute-lft-out unswap-sqr
Counts
4 → 75
Calls
4 calls:
Slowest
15.0ms
(* (tan x) (tan eps))
12.0ms
(+ (tan x) (tan eps))
10.0ms
(- 1 (* (tan x) (tan eps)))
0.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series858.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
438.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
161.0ms
(- 1 (* (tan x) (tan eps)))
139.0ms
(+ (tan x) (tan eps))
120.0ms
(* (tan x) (tan eps))

simplify3.2s

Counts
41 → 87
Calls
41 calls:
Slowest
466.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
341.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))
335.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
285.0ms
(- (+ (/ (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)))
277.0ms
(- (+ (/ (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)))

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.5b

localize73.0ms

Local error

Found 4 expressions with local error:

4.3b
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (- (tan x)))
0.2b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(* (sin x) (sin eps))
0.1b
(+ (tan x) (tan eps))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×pow1 add-log-exp
5×prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×tan-quot sin-mult
1×+-commutative clear-num associate-/r* sum-log frac-2neg flip3-+ times-frac pow-prod-down frac-add associate-/r/ cos-mult *-commutative flip-+ fma-udef div-inv distribute-lft-out associate-/l* unswap-sqr associate-/l/
Counts
4 → 78
Calls
4 calls:
Slowest
29.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
14.0ms
(* (sin x) (sin eps))
8.0ms
(+ (tan x) (tan eps))
0.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (- (tan x)))

series769.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
434.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (- (tan x)))
142.0ms
(+ (tan x) (tan eps))
122.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
71.0ms
(* (sin x) (sin eps))

simplify5.6s

Counts
42 → 90
Calls
42 calls:
Slowest
862.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
720.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
695.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
561.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
392.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.5b

regimes583.0ms

Accuracy

90.6% (0.7b remaining)

Error of 15.5b against oracle of 14.8b and baseline of 22.7b

bsearch277.0ms

end0.0ms

sample12.1s

Algorithm
intervals
Results
5.8s3251×body1280valid
3.0s1862×body640valid
2.0s660×body2560valid
695.0ms781×body320valid
249.0ms1093×body80valid
190.0ms353×body160valid