Details

Time bar (total: 2.8m)

sample289.0ms

Algorithm
intervals
Results
111.0ms331×body80valid
64.0ms67×body10240exit
54.0ms58×body1280valid
27.0ms45×body640valid
6.0ms16×body320valid
2.0ms7×body160valid

simplify346.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
346.0ms
(/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2)

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize75.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (/ (exp (* x (+ -1 eps))) eps) (- (exp (* x (+ -1 eps))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
0.0b
(* x (+ -1 eps))
0.0b
(* x (+ -1 eps))
0.0b
(/ (exp (* x (+ -1 eps))) eps)

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
61×*-un-lft-identity
38×add-cube-cbrt
35×times-frac
33×associate-+r+
30×prod-diff
26×exp-sum
19×fma-def
15×distribute-rgt-in distribute-lft-in
13×add-log-exp
10×add-cbrt-cube difference-of-squares
9×add-exp-log
8×pow1 associate-*r* distribute-lft-out--
6×associate-*l*
5×distribute-lft-out associate-/l*
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u
3×associate-/r* sum-log flip3-+ diff-log flip-+
2×pow-prod-down frac-add prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
1×cbrt-undiv +-commutative clear-num associate-+r- sub-neg frac-2neg flip3-- div-exp flip-- associate--r-
Counts
4 → 164
Calls
4 calls:
Slowest
322.0ms
(+ (/ (exp (* x (+ -1 eps))) eps) (- (exp (* x (+ -1 eps))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
25.0ms
(* x (+ -1 eps))
25.0ms
(* x (+ -1 eps))
18.0ms
(/ (exp (* x (+ -1 eps))) eps)

series258.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(+ (/ (exp (* x (+ -1 eps))) eps) (- (exp (* x (+ -1 eps))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
43.0ms
(* x (+ -1 eps))
39.0ms
(* x (+ -1 eps))
38.0ms
(/ (exp (* x (+ -1 eps))) eps)

simplify22.1s

Counts
142 → 176
Calls
142 calls:
Slowest
719.0ms
(fma (- (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) 1 (* (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))) 1))
519.0ms
(- (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
485.0ms
(/ (* (* (exp (* x (+ -1 eps))) (exp (* x (+ -1 eps)))) (exp (* x (+ -1 eps)))) (* (* eps eps) eps))
407.0ms
(- (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
399.0ms
(- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))

prune2.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize72.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (/ (exp (* (- -1 eps) x)) eps) (/ (exp (* (+ -1 eps) x)) eps))
0.1b
(exp (- (+ (exp (* (+ -1 eps) x)) (exp (* (- -1 eps) x))) (- (/ (exp (* (- -1 eps) x)) eps) (/ (exp (* (+ -1 eps) x)) eps))))
0.0b
(* (+ -1 eps) x)
0.0b
(* (+ -1 eps) x)

rewrite593.0ms

Algorithm
rewrite-expression-head
Rules
304×*-un-lft-identity
293×times-frac
290×add-sqr-sqrt
224×add-cube-cbrt
217×prod-diff
52×exp-sum
37×div-inv
26×distribute-lft-out--
21×difference-of-squares
19×add-log-exp
16×distribute-lft-out
13×fma-neg
8×pow1 exp-prod add-cbrt-cube associate-*l* add-exp-log
7×diff-log
6×associate-*r*
5×distribute-rgt-out-- rem-exp-log
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u
2×sum-log sub-neg flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×flip3-- exp-diff associate--l+ frac-sub flip-- sub-div associate--r-
Counts
4 → 332
Calls
4 calls:
Slowest
480.0ms
(exp (- (+ (exp (* (+ -1 eps) x)) (exp (* (- -1 eps) x))) (- (/ (exp (* (- -1 eps) x)) eps) (/ (exp (* (+ -1 eps) x)) eps))))
41.0ms
(- (/ (exp (* (- -1 eps) x)) eps) (/ (exp (* (+ -1 eps) x)) eps))
29.0ms
(* (+ -1 eps) x)
27.0ms
(* (+ -1 eps) x)

series385.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(exp (- (+ (exp (* (+ -1 eps) x)) (exp (* (- -1 eps) x))) (- (/ (exp (* (- -1 eps) x)) eps) (/ (exp (* (+ -1 eps) x)) eps))))
106.0ms
(- (/ (exp (* (- -1 eps) x)) eps) (/ (exp (* (+ -1 eps) x)) eps))
37.0ms
(* (+ -1 eps) x)
32.0ms
(* (+ -1 eps) x)

simplify2.0m

Counts
471 → 344
Calls
471 calls:
Slowest
747.0ms
(fma (- (/ (exp (* (+ -1 eps) x)) (sqrt eps))) (/ 1 (sqrt eps)) (* (/ (exp (* (+ -1 eps) x)) (sqrt eps)) (/ 1 (sqrt eps))))
714.0ms
(fma (/ (sqrt (exp (* (- -1 eps) x))) (* (cbrt eps) (cbrt eps))) (/ (sqrt (exp (* (- -1 eps) x))) (cbrt eps)) (- (* (/ (cbrt (exp (* (+ -1 eps) x))) (cbrt eps)) (/ (* (cbrt (exp (* (+ -1 eps) x))) (cbrt (exp (* (+ -1 eps) x)))) (* (cbrt eps) (cbrt eps))))))
657.0ms
(- (+ (/ (* (exp (* (- eps 1) x)) (exp (+ (exp (* (- eps 1) x)) (exp (* -1 (* x (+ eps 1))))))) eps) (+ (* 1/2 (/ (* (pow (exp (* (- eps 1) x)) 2) (exp (+ (exp (* (- eps 1) x)) (exp (* -1 (* x (+ eps 1))))))) (pow eps 2))) (+ (exp (+ (exp (* (- eps 1) x)) (exp (* -1 (* x (+ eps 1)))))) (* 1/2 (/ (* (pow (exp (* -1 (* x (+ eps 1)))) 2) (exp (+ (exp (* (- eps 1) x)) (exp (* -1 (* x (+ eps 1))))))) (pow eps 2)))))) (+ (/ (* (exp (* -1 (* x (+ eps 1)))) (exp (+ (exp (* (- eps 1) x)) (exp (* -1 (* x (+ eps 1))))))) eps) (/ (* (exp (* (- eps 1) x)) (* (exp (* -1 (* x (+ eps 1)))) (exp (+ (exp (* (- eps 1) x)) (exp (* -1 (* x (+ eps 1)))))))) (pow eps 2))))
651.0ms
(exp (fma 1 (+ (exp (* (+ -1 eps) x)) (exp (* (- -1 eps) x))) (- (* (- (/ (sqrt (exp (* (- -1 eps) x))) (sqrt eps)) (sqrt (/ (exp (* (+ -1 eps) x)) eps))) (+ (/ (sqrt (exp (* (- -1 eps) x))) (sqrt eps)) (sqrt (/ (exp (* (+ -1 eps) x)) eps)))))))
640.0ms
(* (* (* (+ -1 eps) (+ -1 eps)) (+ -1 eps)) (* (* x x) x))

prune6.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

10.9b
(log (fma (exp 2) (- (* x (* (* x x) 2/3)) (* x x)) (exp 2)))
6.4b
(- (* x (* (* x x) 2/3)) (* x x))
0.1b
(* (* x x) 2/3)
0.1b
(* x (* (* x x) 2/3))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log
18×add-cbrt-cube
9×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×add-log-exp
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u
3×log-prod
2×*-commutative
1×sub-neg flip3-- fma-neg diff-log rem-log-exp prod-diff log-pow flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 79
Calls
4 calls:
Slowest
52.0ms
(- (* x (* (* x x) 2/3)) (* x x))
47.0ms
(* x (* (* x x) 2/3))
15.0ms
(* (* x x) 2/3)
2.0ms
(log (fma (exp 2) (- (* x (* (* x x) 2/3)) (* x x)) (exp 2)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(log (fma (exp 2) (- (* x (* (* x x) 2/3)) (* x x)) (exp 2)))
110.0ms
(- (* x (* (* x x) 2/3)) (* x x))
53.0ms
(* x (* (* x x) 2/3))
27.0ms
(* (* x x) 2/3)

simplify4.4s

Counts
41 → 91
Calls
41 calls:
Slowest
603.0ms
(* (* (* x x) x) (* (* (* (* x x) 2/3) (* (* x x) 2/3)) (* (* x x) 2/3)))
532.0ms
(* (* (* x x) x) (* (* (* (* x x) (* x x)) (* x x)) (* (* 2/3 2/3) 2/3)))
264.0ms
(log (sqrt (fma (exp 2) (- (* x (* (* x x) 2/3)) (* x x)) (exp 2))))
256.0ms
(/ (exp (* x (* (* x x) 2/3))) (exp (* x x)))
239.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* 2/3 2/3) 2/3))

prune922.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

6.4b
(fma (* x (* x x)) 2/3 (- 2 (* x x)))
0.1b
(* x (* x x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
7×add-cbrt-cube add-exp-log
5×pow-prod-up
4×add-sqr-sqrt
3×*-un-lft-identity associate-*l* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×pow2 pow-plus cube-unmult associate-*r* pow-sqr *-commutative fma-udef unswap-sqr
Counts
2 → 38
Calls
2 calls:
Slowest
18.0ms
(* x (* x x))
0.0ms
(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series119.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
60.0ms
(* x (* x x))
59.0ms
(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify1.8s

Counts
20 → 44
Calls
20 calls:
Slowest
589.0ms
(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
451.0ms
(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
232.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
205.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
198.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune374.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes118.0ms

Accuracy

0% (0.5b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 1.1b

bsearch5.0ms

end0.0ms

sample11.6s

Algorithm
intervals
Results
3.5s1948×body10240exit
3.4s10243×body80valid
2.3s1752×body1280valid
1.4s1205×body640valid
392.0ms659×body320valid
136.0ms325×body160valid