Details

Time bar (total: 1.0m)

sample371.0ms

Algorithm
intervals
Results
212.0ms103×body1280valid
72.0ms70×body640valid
43.0ms16×body2560valid
18.0ms25×body320valid
9.0ms35×body80valid
4.0ms7×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: 35.4b

localize39.0ms

Local error

Found 2 expressions with local error:

4.4b
(tan (+ x eps))
1.0b
(- (tan (+ x eps)) (tan x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity tan-quot add-log-exp
2×pow1 tan-sum add-cbrt-cube add-exp-log frac-sub add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 27
Calls
2 calls:
Slowest
19.0ms
(- (tan (+ x eps)) (tan x))
5.0ms
(tan (+ x eps))

series176.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
116.0ms
(- (tan (+ x eps)) (tan x))
60.0ms
(tan (+ x eps))

simplify1.4s

Counts
15 → 33
Calls
15 calls:
Slowest
472.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
407.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
200.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
139.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
48.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune394.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.3b

localize21.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (/ (+ (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))))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1
5×distribute-lft-out
4×insert-posit16 associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×flip3-+ flip3-- frac-add associate-/r/ flip-+ 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 div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
84.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
42.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
13.0ms
(* (tan x) (tan eps))
13.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
552.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
289.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
147.0ms
(* (tan x) (tan eps))
139.0ms
(+ (tan x) (tan eps))

simplify5.2s

Counts
74 → 102
Calls
74 calls:
Slowest
452.0ms
(/ (* (* (+ (tan x) (tan eps)) (+ (tan x) (tan eps))) (+ (tan x) (tan eps))) (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))))
417.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
415.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
383.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
374.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.2b

localize42.0ms

Local error

Found 4 expressions with local error:

4.1b
(log (exp (* (tan x) (tan eps))))
2.8b
(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(exp (* (tan x) (tan eps)))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×*-un-lft-identity add-log-exp
7×pow1 add-cube-cbrt
6×add-cbrt-cube add-exp-log
5×tan-quot
4×insert-posit16
3×log-prod associate-*r* associate-*l* log-pow
2×exp-prod exp-to-pow difference-of-squares
1×frac-times sub-neg times-frac flip3-- diff-log rem-log-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-- distribute-lft-out-- unswap-sqr rem-exp-log
Counts
4 → 65
Calls
4 calls:
Slowest
143.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
28.0ms
(exp (* (tan x) (tan eps)))
27.0ms
(* (tan x) (tan eps))
15.0ms
(log (exp (* (tan x) (tan eps))))

series981.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
529.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
173.0ms
(exp (* (tan x) (tan eps)))
147.0ms
(* (tan x) (tan eps))
132.0ms
(log (exp (* (tan x) (tan eps))))

simplify4.8s

Counts
43 → 77
Calls
43 calls:
Slowest
433.0ms
(* (- 1 (log (exp (* (tan x) (tan eps))))) (cos x))
313.0ms
(- (+ (/ (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)))
301.0ms
(- (+ (/ (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)))
291.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
290.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (log (exp (* (tan x) (tan eps))))) (sin x)))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.2b

localize48.0ms

Local error

Found 4 expressions with local error:

5.7b
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
0.3b
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
0.3b
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
104×*-un-lft-identity
83×add-sqr-sqrt
67×add-cube-cbrt
23×associate-/r*
19×add-exp-log
16×associate-/r/ distribute-lft-out
15×tan-quot
13×add-cbrt-cube
8×div-exp
7×pow1 div-inv
6×associate-/l* add-log-exp
5×flip3-+ frac-add flip-+ difference-of-squares
4×cbrt-undiv insert-posit16
3×associate-*r* associate-*l*
2×rec-exp clear-num frac-2neg flip3-- 1-exp flip-- distribute-lft-out-- associate-/l/
1×frac-times sub-neg diff-log div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod pow-flip inv-pow unswap-sqr
Counts
4 → 182
Calls
4 calls:
Slowest
121.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
16.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
16.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
14.0ms
(* (tan x) (tan eps))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
477.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
362.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
348.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
129.0ms
(* (tan x) (tan eps))

simplify23.6s

Counts
222 → 194
Calls
222 calls:
Slowest
690.0ms
(/ (* (* 1 1) 1) (* (* (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))) (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))))
656.0ms
(+ (sqrt (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))) (sqrt (tan x)))
448.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
391.0ms
(/ (cbrt 1) (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
372.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.2b

regimes265.0ms

Accuracy

90.3% (0.7b remaining)

Error of 15.0b against oracle of 14.3b and baseline of 21.9b

bsearch406.0ms

end0.0ms

sample15.0s

Algorithm
intervals
Results
7.9s3329×body1280valid
3.2s1876×body640valid
2.2s619×body2560valid
791.0ms754×body320valid
393.0ms1076×body80valid
248.0ms346×body160valid