Details

Time bar (total: 53.8s)

sample586.0ms

Algorithm
intervals
Results
168.0ms118×body1280valid
164.0ms79×body2560valid
148.0ms68×body10240exit
57.0ms37×body640valid
16.0ms324×pre80true
5.0ms8×body320valid
2.0ms12×body80valid
0.0ms2×body160valid

simplify289.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
289.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.4b

localize55.0ms

Local error

Found 4 expressions with local error:

30.7b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
16.8b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
8×associate-/l*
7×cbrt-undiv div-exp
6×pow1 associate-/r* div-inv
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l* prod-exp cbrt-unprod
2×clear-num frac-2neg
1×expm1-log1p pow-prod-down *-commutative expm1-udef unswap-sqr associate-/l/
Counts
4 → 108
Calls
4 calls:
Slowest
14.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
10.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
5.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* (+ a b) eps))

series955.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
566.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
180.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
160.0ms
(* (expm1 (* (+ a b) eps)) eps)
49.0ms
(expm1 (* (+ a b) eps))

simplify9.4s

Counts
94 → 120
Calls
94 calls:
Slowest
536.0ms
(/ (/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
513.0ms
(/ (/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
414.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
403.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
358.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune1.9s

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))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×times-frac
13×fma-def
10×add-sqr-sqrt add-cube-cbrt
7×distribute-lft-out
5×div-inv
3×add-log-exp
1×expm1-log1p-u pow1 +-commutative sum-log flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 log1p-expm1-u
Counts
1 → 35
Calls
1 calls:
Slowest
22.0ms
(+ (/ 1 a) (/ 1 b))

series20.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
20.0ms
(+ (/ 1 a) (/ 1 b))

simplify355.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
53.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
21.0ms
(+ (/ (sqrt 1) a) (/ (sqrt 1) b))
20.0ms
(+ (/ (cbrt 1) a) (/ (cbrt 1) b))
18.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(+ (/ 1 a) (/ 1 b))

prune282.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

15.5b
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
6.1b
(/ (* eps b) a)
0.0b
(+ (/ (* eps b) a) eps)
0.0b
(expm1 (* eps b))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
18×times-frac
17×add-sqr-sqrt add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×fma-def
6×associate-/r* add-log-exp
5×log1p-expm1-u distribute-lft-out associate-/l*
4×expm1-log1p-u pow1 insert-posit16
3×cbrt-undiv div-exp div-inv
2×clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×+-commutative expm1-log1p sum-log prod-exp cbrt-unprod expm1-udef
Counts
4 → 94
Calls
4 calls:
Slowest
40.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
21.0ms
(+ (/ (* eps b) a) eps)
10.0ms
(/ (* eps b) a)
1.0ms
(expm1 (* eps b))

series231.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
53.0ms
(expm1 (* eps b))
37.0ms
(/ (* eps b) a)
34.0ms
(+ (/ (* eps b) a) eps)

simplify4.3s

Counts
66 → 106
Calls
66 calls:
Slowest
516.0ms
(+ (pow (/ (* eps b) a) 3) (pow eps 3))
314.0ms
(- (* (/ (* eps b) a) (/ (* eps b) a)) (* eps eps))
281.0ms
(- (+ (/ 1 b) (/ 1 a)) (* 1/2 (/ (* eps b) a)))
263.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))
228.0ms
(/ (* (* (* eps b) (* eps b)) (* eps b)) (* (* a a) a))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

23.2b
(* (expm1 (* (+ b a) eps)) (/ (/ eps (expm1 (* eps a))) (expm1 (* eps b))))
17.0b
(/ eps (expm1 (* eps a)))
4.5b
(/ (/ eps (expm1 (* eps a))) (expm1 (* eps b)))
0.0b
(expm1 (* (+ b a) eps))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
99×add-sqr-sqrt
90×*-un-lft-identity add-cube-cbrt
43×associate-*r*
20×add-cbrt-cube add-exp-log
16×associate-/l*
10×div-inv
7×cbrt-undiv div-exp
6×pow1 associate-/r*
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*l* prod-exp cbrt-unprod unswap-sqr
2×clear-num frac-2neg
1×expm1-log1p pow-prod-down associate-*r/ *-commutative expm1-udef associate-/l/
Counts
4 → 183
Calls
4 calls:
Slowest
25.0ms
(* (expm1 (* (+ b a) eps)) (/ (/ eps (expm1 (* eps a))) (expm1 (* eps b))))
21.0ms
(/ (/ eps (expm1 (* eps a))) (expm1 (* eps b)))
8.0ms
(/ eps (expm1 (* eps a)))
1.0ms
(expm1 (* (+ b a) eps))

series966.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
639.0ms
(* (expm1 (* (+ b a) eps)) (/ (/ eps (expm1 (* eps a))) (expm1 (* eps b))))
170.0ms
(/ (/ eps (expm1 (* eps a))) (expm1 (* eps b)))
81.0ms
(expm1 (* (+ b a) eps))
75.0ms
(/ eps (expm1 (* eps a)))

simplify11.2s

Counts
193 → 195
Calls
193 calls:
Slowest
464.0ms
(/ (* (* eps eps) eps) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))))
461.0ms
(/ (* (* (/ eps (expm1 (* eps a))) (/ eps (expm1 (* eps a)))) (/ eps (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
359.0ms
(* (* (* (expm1 (* (+ b a) eps)) (expm1 (* (+ b a) eps))) (expm1 (* (+ b a) eps))) (/ (/ (* (* eps eps) eps) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b)))))
352.0ms
(/ (/ (* (cbrt eps) (cbrt eps)) (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a))))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))
334.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))

prune2.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

0% (3.3b remaining)

Error of 3.3b against oracle of 0.0b and baseline of 3.3b

bsearch2.0ms

end0.0ms

sample19.4s

Algorithm
intervals
Results
6.2s2547×body2560valid
5.4s3495×body1280valid
5.1s1963×body10240exit
1.4s1035×body640valid
607.0ms9966×pre80true
251.0ms337×body320valid
80.0ms452×body80valid
73.0ms137×body160valid