Details

Time bar (total: 1.2m)

sample633.0ms

Algorithm
intervals
Results
230.0ms124×body1280valid
164.0ms66×body10240exit
158.0ms78×body2560valid
27.0ms26×body640valid
17.0ms322×pre80true
6.0ms10×body320valid
3.0ms17×body80valid
0.0ms1×body160valid

simplify302.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
302.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.7b

localize71.0ms

Local error

Found 4 expressions with local error:

4.3b
(- (exp (* (+ a b) eps)) 1)
2.9b
(- (exp (* b eps)) 1)
1.5b
(- (exp (* a eps)) 1)
1.0b
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×*-un-lft-identity
10×add-log-exp difference-of-squares
9×flip3-- flip--
7×associate-*r* associate-*l*
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
5×sub-neg difference-of-sqr-1 distribute-lft-out--
4×frac-times insert-posit16
3×diff-log
2×distribute-rgt-in distribute-lft-in associate-*l/ associate-*r/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
96.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
27.0ms
(- (exp (* (+ a b) eps)) 1)
25.0ms
(- (exp (* b eps)) 1)
24.0ms
(- (exp (* a eps)) 1)

series231.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(- (exp (* (+ a b) eps)) 1)
70.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
46.0ms
(- (exp (* a eps)) 1)
36.0ms
(- (exp (* b eps)) 1)

simplify12.5s

Counts
66 → 102
Calls
66 calls:
Slowest
647.0ms
(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))
432.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
424.0ms
(* (+ (exp (* a eps)) 1) (+ (exp (* b eps)) 1))
410.0ms
(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (exp (* b eps)) 1))
395.0ms
(+ (* (exp (* b eps)) (exp (* b eps))) (+ (* 1 1) (* (exp (* b eps)) 1)))

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 46.4b

localize112.0ms

Local error

Found 4 expressions with local error:

4.3b
(- (exp (* (+ a b) eps)) 1)
3.4b
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
2.9b
(- (exp (* b eps)) 1)
2.6b
(* (* 1/6 a) (* (* a eps) (* a eps)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
57×add-cbrt-cube add-exp-log
45×pow1
35×prod-exp cbrt-unprod
31×pow-prod-down
12×add-sqr-sqrt
10×*-un-lft-identity
8×associate-/r/ add-log-exp
6×flip3-- flip--
4×frac-times cbrt-undiv div-exp associate-*r/ add-cube-cbrt insert-posit16 difference-of-squares
3×flip3-+ flip-+
2×sub-neg diff-log difference-of-sqr-1 associate-*l/ distribute-lft-out-- associate-/l/
1×clear-num associate-/r* frac-2neg times-frac associate-*r* associate-*l* *-commutative div-inv associate-/l*
Counts
4 → 107
Calls
4 calls:
Slowest
1.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
77.0ms
(* (* 1/6 a) (* (* a eps) (* a eps)))
22.0ms
(- (exp (* b eps)) 1)
16.0ms
(- (exp (* (+ a b) eps)) 1)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
82.0ms
(- (exp (* (+ a b) eps)) 1)
75.0ms
(* (* 1/6 a) (* (* a eps) (* a eps)))
60.0ms
(- (exp (* b eps)) 1)

simplify18.9s

Counts
78 → 119
Calls
78 calls:
Slowest
920.0ms
(+ (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps))) (- (* (* 1/2 (* (* a eps) (* a eps))) (* 1/2 (* (* a eps) (* a eps)))) (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))))
750.0ms
(* (+ (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps))) (- (* (* 1/2 (* (* a eps) (* a eps))) (* 1/2 (* (* a eps) (* a eps)))) (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))))) (+ (exp (* b eps)) 1))
458.0ms
(* (* (* (* 1/6 1/6) 1/6) (* (* a a) a)) (* (* (* (* a a) a) (* (* eps eps) eps)) (* (* (* a eps) (* a eps)) (* a eps))))
434.0ms
(/ eps (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))))
399.0ms
(* (* (* (* 1/6 a) (* 1/6 a)) (* 1/6 a)) (* (* (* (* a a) a) (* (* eps eps) eps)) (* (* (* a eps) (* a eps)) (* a eps))))

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (/ 1 a) (/ 1 b))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
7×distribute-lft-out
6×times-frac
4×div-inv
3×add-sqr-sqrt add-cube-cbrt add-log-exp
1×pow1 +-commutative sum-log flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16
Counts
1 → 20
Calls
1 calls:
Slowest
11.0ms
(+ (/ 1 a) (/ 1 b))

series18.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
18.0ms
(+ (/ 1 a) (/ 1 b))

simplify228.0ms

Counts
16 → 23
Calls
16 calls:
Slowest
29.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
22.0ms
(+ (/ 1 a) (/ 1 b))
19.0ms
(+ (/ 1 a) (/ 1 b))
17.0ms
(+ (/ 1 b) (/ 1 a))
17.0ms
(+ (/ 1 a) (/ 1 b))

prune196.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.5b
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
139×*-un-lft-identity
114×cbrt-prod
81×distribute-lft-out
60×div-inv
42×times-frac
37×add-sqr-sqrt
33×cbrt-div swap-sqr
29×add-cube-cbrt
13×associate-*r* associate-*l*
11×pow1 flip3-+ frac-add flip-+
9×frac-times pow1/3
6×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
3×associate-*l/ associate-*r/
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 163
Calls
4 calls:
Slowest
120.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
14.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
13.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
9.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
134.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
105.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
96.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

simplify10.1s

Counts
187 → 175
Calls
187 calls:
Slowest
389.0ms
(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (+ (* 1 b) (* a 1))))
345.0ms
(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (+ (/ 1 a) (/ 1 b))))
336.0ms
(* (cbrt (+ (* 1 b) (* a 1))) (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
332.0ms
(cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))
320.0ms
(cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))

prune2.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes191.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch2.0ms

end0.0ms

sample20.4s

Algorithm
intervals
Results
6.5s2594×body2560valid
6.1s3482×body1280valid
4.6s1942×body10240exit
959.0ms1016×body640valid
907.0ms9946×pre80true
754.0ms344×body320valid
120.0ms442×body80valid
48.0ms126×body160valid