Details

Time bar (total: 32.8s)

sample566.0ms

Algorithm
intervals
Results
193.0ms112×body1280valid
187.0ms85×body2560valid
111.0ms47×body10240exit
22.0ms24×body640valid
15.0ms303×pre80true
8.0ms11×body320valid
4.0ms18×body80valid
3.0ms6×body160valid

simplify640.0ms

Calls
1 calls:
Slowest
639.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize36.0ms

Local error

Found 4 expressions with local error:

40.8b
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
0.3b
(* (expm1 (* (+ a b) eps)) eps)
0.3b
(* (expm1 (* eps b)) (expm1 (* eps a)))
0.0b
(expm1 (* eps a))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube add-exp-log
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r*
2×cbrt-undiv div-exp prod-exp *-commutative cbrt-unprod
1×expm1-log1p clear-num associate-/r* frac-2neg times-frac pow-prod-down div-inv associate-/l* expm1-udef
Calls
4 calls:
Slowest
9.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
4.0ms
(* (expm1 (* eps b)) (expm1 (* eps a)))
3.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* eps a))

series829.0ms

Calls
4 calls:
Slowest
593.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
123.0ms
(* (expm1 (* (+ a b) eps)) eps)
60.0ms
(* (expm1 (* eps b)) (expm1 (* eps a)))
53.0ms
(expm1 (* eps a))

simplify3.5s

Calls
31 calls:
Slowest
706.0ms
(/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (expm1 (* eps b)) (expm1 (* eps a))) (* (expm1 (* eps b)) (expm1 (* eps a)))) (* (expm1 (* eps b)) (expm1 (* eps a)))))
586.0ms
(/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))))
334.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
325.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
302.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* 1/6 (* (pow a 3) (pow eps 3))) (* a eps)))

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×div-inv
4×fma-def distribute-lft-out
3×add-log-exp
2×add-sqr-sqrt add-cube-cbrt
1×expm1-log1p-u pow1 +-commutative sum-log flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 log1p-expm1-u
Calls
1 calls:
Slowest
4.0ms
(+ (/ 1 a) (/ 1 b))

series12.0ms

Calls
1 calls:
Slowest
12.0ms
(+ (/ 1 a) (/ 1 b))

simplify171.0ms

Calls
12 calls:
Slowest
27.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
19.0ms
(+ (/ 1 b) (/ 1 a))
18.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(+ (/ 1 b) (/ 1 a))
17.0ms
(+ (/ 1 a) (/ 1 b))

prune185.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 1 expressions with local error:

15.6b
(/ (+ b a) (* a b))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity times-frac add-cbrt-cube add-exp-log add-cube-cbrt associate-/l*
2×associate-/l/
1×expm1-log1p-u pow1 cbrt-undiv clear-num associate-/r* frac-2neg flip3-+ div-exp flip-+ insert-posit16 log1p-expm1-u div-inv add-log-exp
Calls
1 calls:
Slowest
7.0ms
(/ (+ b a) (* a b))

series72.0ms

Calls
1 calls:
Slowest
72.0ms
(/ (+ b a) (* a b))

simplify395.0ms

Calls
15 calls:
Slowest
175.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
61.0ms
(- (log (+ b a)) (log (* a b)))
42.0ms
(- (* b b) (* a a))
23.0ms
(+ (pow b 3) (pow a 3))
18.0ms
(+ (/ 1 a) (/ 1 b))

prune253.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

17.1b
(/ eps (expm1 (* eps a)))
13.8b
(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
5.2b
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
0.0b
(expm1 (* eps a))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
13×associate-*l*
11×add-cbrt-cube add-exp-log
6×pow1 associate-/r*
5×log1p-expm1-u
4×expm1-log1p-u associate-*r* insert-posit16 div-inv add-log-exp
3×associate-/l*
2×cbrt-undiv clear-num frac-2neg div-exp prod-exp cbrt-unprod expm1-udef
1×frac-times expm1-log1p div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative
Calls
4 calls:
Slowest
14.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
8.0ms
(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
1.0ms
(/ eps (expm1 (* eps a)))
1.0ms
(expm1 (* eps a))

series844.0ms

Calls
4 calls:
Slowest
614.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
113.0ms
(/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))
78.0ms
(/ eps (expm1 (* eps a)))
39.0ms
(expm1 (* eps a))

simplify4.0s

Calls
67 calls:
Slowest
604.0ms
(* (* (* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))) (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))) (* (* (/ eps (expm1 (* eps a))) (/ eps (expm1 (* eps a)))) (/ eps (expm1 (* eps a)))))
357.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
322.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
287.0ms
(* (/ (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b)))) (* (* (/ eps (expm1 (* eps a))) (/ eps (expm1 (* eps a)))) (/ eps (expm1 (* eps a)))))
241.0ms
(+ (log (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b)))) (log (/ eps (expm1 (* eps a)))))

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes143.0ms

Accuracy

6.2% (3.3b remaining)

Error of 3.3b against oracle of 0.0b and baseline of 3.5b

bsearch397.0ms

end0.0ms

sample18.4s

Algorithm
intervals
Results
5.6s2621×body2560valid
5.4s3448×body1280valid
4.9s1947×body10240exit
917.0ms9948×pre80true
873.0ms993×body640valid
274.0ms330×body320valid
82.0ms476×body80valid
49.0ms133×body160valid