Details

Time bar (total: 8.0m)

sample648.0ms

Algorithm
intervals
Results
221.0ms72×body10240exit
181.0ms81×body2560valid
163.0ms114×body1280valid
27.0ms27×body640valid
17.0ms328×pre80true
7.0ms13×body320valid
4.0ms18×body80valid
1.0ms3×body160valid

simplify375.0ms

Calls
1 calls:
Slowest
374.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.5b

localize69.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (exp (* (+ a b) eps)) 1)
2.2b
(- (exp (* b eps)) 1)
1.8b
(- (exp (* a eps)) 1)
0.7b
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))

rewrite445.0ms

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
Calls
4 calls:
Slowest
195.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
180.0ms
(- (exp (* (+ a b) eps)) 1)
35.0ms
(- (exp (* a eps)) 1)
34.0ms
(- (exp (* b eps)) 1)

series235.0ms

Calls
4 calls:
Slowest
82.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
75.0ms
(- (exp (* (+ a b) eps)) 1)
42.0ms
(- (exp (* a eps)) 1)
35.0ms
(- (exp (* b eps)) 1)

simplify13.5s

Calls
66 calls:
Slowest
674.0ms
(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))
497.0ms
(* (+ (exp (* a eps)) 1) (+ (exp (* b eps)) 1))
493.0ms
(* (- (exp (* eps b)) 1) (- (exp (* a eps)) 1))
486.0ms
(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (exp (* b eps)) 1))
429.0ms
(+ (* (exp (* b eps)) (exp (* b eps))) (+ (* 1 1) (* (exp (* b eps)) 1)))

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 45.8b

localize71.0ms

Local error

Found 4 expressions with local error:

3.7b
(/ (* 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 (* (+ a b) eps)) 1)
2.7b
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
2.4b
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))

rewrite49.4s

Algorithm
rewrite-expression-head
Rules
1735×associate-*r*
1186×*-un-lft-identity
1073×associate-*l*
746×add-sqr-sqrt
672×times-frac
324×distribute-lft-out
288×distribute-lft1-in distribute-rgt-out
217×*-commutative
204×add-cube-cbrt
187×unswap-sqr
124×difference-of-squares
71×add-cbrt-cube add-exp-log
62×difference-of-sqr-1 distribute-lft-out--
59×pow1
47×prod-exp cbrt-unprod
43×pow-prod-down
42×associate-/r*
22×swap-sqr
16×associate-/l*
8×frac-times flip3-- associate-/r/ flip--
6×flip3-+ associate-*r/ flip-+ add-log-exp
4×cbrt-undiv div-exp associate-*l/ insert-posit16
3×sub-neg
2×distribute-rgt-in distribute-lft-in associate-/l/
1×clear-num frac-2neg diff-log div-inv
Calls
4 calls:
Slowest
30.2s
(/ (* 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)))
18.5s
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
580.0ms
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))
139.0ms
(- (exp (* (+ a b) eps)) 1)

series1.5s

Calls
4 calls:
Slowest
1.2s
(/ (* 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)))
135.0ms
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
104.0ms
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))
79.0ms
(- (exp (* (+ a b) eps)) 1)

simplify6.4m

Calls
1634 calls:
Slowest
1.3s
(* (* (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* 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))))) (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))) (* (* (- (exp (* b eps)) 1) (- (exp (* b eps)) 1)) (- (exp (* b eps)) 1)))
997.0ms
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))
977.0ms
(/ eps (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) 1))) 1) (* 1/2 (* a eps))) (- (exp (* b eps)) 1)))
925.0ms
(/ (* (cbrt (* eps (- (exp (* (+ a b) eps)) 1))) (cbrt (* eps (- (exp (* (+ a b) eps)) 1)))) (* a eps))
881.0ms
(* (+ (* (+ (* 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))

prune17.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-add
54×associate-/r* associate-/l*
49×*-un-lft-identity
39×add-sqr-sqrt add-cube-cbrt
18×clear-num frac-2neg
7×distribute-lft-out
6×times-frac
4×div-inv
3×add-log-exp
1×pow1 +-commutative sum-log flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
Calls
1 calls:
Slowest
16.0ms
(+ (/ 1 a) (/ 1 b))

series21.0ms

Calls
1 calls:
Slowest
21.0ms
(+ (/ 1 a) (/ 1 b))

simplify7.0s

Calls
176 calls:
Slowest
508.0ms
(+ (* (/ 1 (* (cbrt a) (cbrt a))) (- b)) (* (cbrt a) (- 1)))
466.0ms
(+ (* (- 1) (cbrt b)) (* (- a) (/ 1 (* (cbrt b) (cbrt b)))))
258.0ms
(+ (* (/ 1 (* (cbrt a) (cbrt a))) (cbrt b)) (* (cbrt a) (/ 1 (* (cbrt b) (cbrt b)))))
244.0ms
(+ (* (/ 1 (* (cbrt a) (cbrt a))) (/ b 1)) (* (cbrt a) 1))
242.0ms
(+ (* (/ 1 (* (cbrt a) (cbrt a))) (/ b 1)) (* (cbrt a) 1))

prune736.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

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))))

rewrite831.0ms

Algorithm
rewrite-expression-head
Rules
14193×cbrt-div
13851×frac-add
9234×associate-/r* associate-/l*
6889×frac-times
6295×*-un-lft-identity
6193×add-sqr-sqrt
6185×add-cube-cbrt
3078×clear-num frac-2neg
171×flip3-+ flip-+
114×cbrt-prod
83×associate-*l/ associate-*r/
81×distribute-lft-out
60×div-inv
42×times-frac
33×swap-sqr
13×associate-*r* associate-*l*
11×pow1
9×pow1/3
8×add-cbrt-cube
6×add-exp-log
4×cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative
Calls
4 calls:
Slowest
104.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
17.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
16.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
15.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

series484.0ms

Calls
4 calls:
Slowest
137.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
130.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
117.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
101.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))