Details

Time bar (total: 1.4m)

sample467.0ms

Algorithm
intervals
Results
145.0ms115×body1280valid
127.0ms69×body2560valid
123.0ms55×body10240exit
33.0ms43×body640valid
13.0ms311×pre80true
4.0ms9×body320valid
3.0ms16×body80valid
2.0ms4×body160valid

simplify265.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
265.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.5b

localize42.0ms

Local error

Found 4 expressions with local error:

3.9b
(- (exp (* (+ a b) eps)) 1)
2.5b
(- (exp (* a eps)) 1)
2.4b
(- (exp (* b eps)) 1)
0.1b
(exp (* (+ a b) eps))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-log-exp
13×*-un-lft-identity
6×difference-of-squares
4×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
3×sub-neg flip3-- diff-log difference-of-sqr-1 flip-- distribute-lft-out--
2×exp-to-pow
1×exp-prod sum-log rem-exp-log
Counts
4 → 63
Calls
4 calls:
Slowest
22.0ms
(- (exp (* b eps)) 1)
19.0ms
(- (exp (* a eps)) 1)
12.0ms
(- (exp (* (+ a b) eps)) 1)
11.0ms
(exp (* (+ a b) eps))

series167.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
69.0ms
(- (exp (* (+ a b) eps)) 1)
42.0ms
(- (exp (* b eps)) 1)
38.0ms
(- (exp (* a eps)) 1)
18.0ms
(exp (* (+ a b) eps))

simplify4.8s

Counts
37 → 75
Calls
37 calls:
Slowest
264.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))
257.0ms
(- (exp (* (+ a b) eps)) 1)
254.0ms
(/ (exp (exp (* (+ a b) eps))) (exp 1))
254.0ms
(/ (exp (exp (* b eps))) (exp 1))
244.0ms
(/ (exp (exp (* a eps))) (exp 1))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 45.8b

localize102.0ms

Local error

Found 4 expressions with local error:

3.9b
(- (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 (- (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)))
2.4b
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))

rewrite4.7s

Algorithm
rewrite-expression-head
Rules
71×add-cbrt-cube add-exp-log
59×pow1
47×prod-exp cbrt-unprod
43×pow-prod-down
17×add-sqr-sqrt
13×*-un-lft-identity
8×frac-times flip3-- associate-*r* associate-/r/ flip--
7×add-cube-cbrt
6×flip3-+ associate-*l* associate-*r/ flip-+ add-log-exp
4×cbrt-undiv div-exp associate-*l/ insert-posit16 difference-of-squares
3×sub-neg
2×distribute-rgt-in distribute-lft-in difference-of-sqr-1 *-commutative distribute-lft-out-- associate-/l/
1×clear-num associate-/r* frac-2neg times-frac diff-log div-inv associate-/l* unswap-sqr
Counts
4 → 130
Calls
4 calls:
Slowest
3.5s
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
878.0ms
(/ (* 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)))
270.0ms
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))
32.0ms
(- (exp (* (+ a b) eps)) 1)

series1.3s

Counts
4 → 12
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)))
125.0ms
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
85.0ms
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))
60.0ms
(- (exp (* (+ a b) eps)) 1)

simplify38.0s

Counts
106 → 142
Calls
106 calls:
Slowest
1.2s
(* (* (* (+ (+ (* 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)))
911.0ms
(* (- (* (+ (* 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))))) (- (exp (* b eps)) 1))
843.0ms
(* (+ (* (+ (* 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))
766.0ms
(* (* (* eps eps) eps) (* (* (* (* 1/6 a) (* (* a eps) (* a eps))) (* (* 1/6 a) (* (* a eps) (* a eps)))) (* (* 1/6 a) (* (* a eps) (* a eps)))))
730.0ms
(* (* (* eps eps) eps) (* (* (* (* 1/6 1/6) 1/6) (* (* a a) a)) (* (* (* (* a a) a) (* (* eps eps) eps)) (* (* (* a eps) (* a eps)) (* a eps)))))

prune2.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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
10.0ms
(+ (/ 1 a) (/ 1 b))

series11.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
11.0ms
(+ (/ 1 a) (/ 1 b))

simplify211.0ms

Counts
16 → 23
Calls
16 calls:
Slowest
20.0ms
(+ (/ 1 a) (/ 1 b))
20.0ms
(+ (/ (cbrt 1) a) (/ (cbrt 1) b))
18.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(+ (/ 1 b) (/ 1 a))
18.0ms
(+ (/ 1 a) (/ 1 b))

prune201.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

3.9b
(- (exp (* (+ a b) eps)) 1)
2.5b
(- (exp (* a eps)) 1)
2.4b
(log (exp (- (exp (* b eps)) 1)))
2.4b
(- (exp (* b eps)) 1)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
18×*-un-lft-identity
10×add-log-exp
8×log-pow difference-of-squares
7×exp-prod
6×add-cube-cbrt
5×pow1 log-prod
4×sub-neg add-cbrt-cube difference-of-sqr-1 add-exp-log insert-posit16 distribute-lft-out--
3×flip3-- diff-log flip--
2×exp-sum
1×log-div exp-diff rem-log-exp
Counts
4 → 74
Calls
4 calls:
Slowest
37.0ms
(log (exp (- (exp (* b eps)) 1)))
16.0ms
(- (exp (* a eps)) 1)
12.0ms
(- (exp (* (+ a b) eps)) 1)
11.0ms
(- (exp (* b eps)) 1)

series176.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
63.0ms
(- (exp (* (+ a b) eps)) 1)
42.0ms
(- (exp (* b eps)) 1)
39.0ms
(- (exp (* a eps)) 1)
32.0ms
(log (exp (- (exp (* b eps)) 1)))

simplify6.6s

Counts
47 → 86
Calls
47 calls:
Slowest
262.0ms
(log (sqrt (exp (- (exp (* b eps)) 1))))
248.0ms
(log (* (cbrt (exp (- (exp (* b eps)) 1))) (cbrt (exp (- (exp (* b eps)) 1)))))
247.0ms
(- (exp (* (+ a b) eps)) 1)
245.0ms
(/ (exp (exp (* (+ a b) eps))) (exp 1))
241.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

-20.5% (3.8b remaining)

Error of 4.0b against oracle of 0.1b and baseline of 3.3b

bsearch451.0ms

end0.0ms

sample21.0s

Algorithm
intervals
Results
7.1s2523×body2560valid
5.7s3457×body1280valid
5.3s2081×body10240exit
1.1s1090×body640valid
1.0s10081×pre80true
223.0ms356×body320valid
86.0ms442×body80valid
78.0ms132×body160valid