Details

Time bar (total: 1.3m)

sample506.0ms

Algorithm
intervals
Results
195.0ms114×body1280valid
135.0ms75×body2560valid
103.0ms55×body10240exit
23.0ms31×body640valid
14.0ms311×pre80true
11.0ms16×body320valid
2.0ms15×body80valid
2.0ms5×body160valid

simplify218.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
218.0ms
(/ (* 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: 30.8b

localize61.0ms

Local error

Found 4 expressions with local error:

26.7b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
14.7b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.3b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite40.0ms

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
18.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
15.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
5.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* (+ a b) eps))

series870.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
547.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
135.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
123.0ms
(* (expm1 (* (+ a b) eps)) eps)
64.0ms
(expm1 (* (+ a b) eps))

simplify9.4s

Counts
94 → 120
Calls
94 calls:
Slowest
690.0ms
(- (log (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))) (log (expm1 (* eps b))))
551.0ms
(/ (/ (* (* (* (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))))
504.0ms
(/ (/ (* (* (* (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))))
432.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
348.0ms
(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

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
20.0ms
(+ (/ 1 a) (/ 1 b))

series13.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
13.0ms
(+ (/ 1 a) (/ 1 b))

simplify337.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
36.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
21.0ms
(+ (/ 1 a) (/ 1 b))
19.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt a))
18.0ms
(+ (/ 1 a) (/ 1 b))

prune290.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 1 expressions with local error:

13.7b
(/ (+ b a) (* a b))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
6×add-cbrt-cube add-exp-log
4×times-frac associate-/l*
3×add-sqr-sqrt add-cube-cbrt
2×cbrt-undiv div-exp distribute-lft-out associate-/l/
1×expm1-log1p-u pow1 clear-num associate-/r* frac-2neg flip3-+ prod-exp cbrt-unprod flip-+ insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 28
Calls
1 calls:
Slowest
26.0ms
(/ (+ b a) (* a b))

series71.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
71.0ms
(/ (+ b a) (* a b))

simplify722.0ms

Counts
19 → 31
Calls
19 calls:
Slowest
226.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
198.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
59.0ms
(- (log (+ b a)) (+ (log a) (log b)))
41.0ms
(- (log (+ b a)) (log (* a b)))
35.0ms
(+ (pow b 3) (pow a 3))

prune225.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

25.5b
(* (/ (* (expm1 (* (+ a b) eps)) eps) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b)))))
16.4b
(/ (* (expm1 (* (+ a b) eps)) eps) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))
15.1b
(cbrt (expm1 (* eps b)))
15.1b
(cbrt (expm1 (* eps b)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
131×add-exp-log
98×add-sqr-sqrt
82×associate-*r*
78×*-un-lft-identity
76×add-cube-cbrt
59×add-cbrt-cube
54×div-exp
49×prod-exp
48×cbrt-prod
31×cbrt-undiv cbrt-unprod
9×div-inv
7×unswap-sqr
6×pow1
5×rec-exp 1-exp associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow1/3
1×frac-times clear-num associate-/r* frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l*
Counts
4 → 201
Calls
4 calls:
Slowest
82.0ms
(* (/ (* (expm1 (* (+ a b) eps)) eps) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b)))))
19.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))
1.0ms
(cbrt (expm1 (* eps b)))
1.0ms
(cbrt (expm1 (* eps b)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
681.0ms
(* (/ (* (expm1 (* (+ a b) eps)) eps) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b)))))
369.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))
137.0ms
(cbrt (expm1 (* eps b)))
120.0ms
(cbrt (expm1 (* eps b)))

simplify36.9s

Counts
175 → 213
Calls
175 calls:
Slowest
1.6s
(* (/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))) (/ (/ (* (* 1 1) 1) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (expm1 (* eps b))))
1.5s
(* (/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))) (* (* (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b)))) (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b))))) (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b))))))
1.4s
(* (/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps)) (* (* (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))) (* (* (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b)))) (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b))))) (/ (/ 1 (expm1 (* eps a))) (cbrt (expm1 (* eps b))))))
1.3s
(* (/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))) (/ (* (* (/ 1 (expm1 (* eps a))) (/ 1 (expm1 (* eps a)))) (/ 1 (expm1 (* eps a)))) (expm1 (* eps b))))
1.2s
(* (/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps)) (* (* (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))) (/ (* (* (/ 1 (expm1 (* eps a))) (/ 1 (expm1 (* eps a)))) (/ 1 (expm1 (* eps a)))) (expm1 (* eps b))))

prune3.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (3.1b remaining)

Error of 3.1b against oracle of 0.0b and baseline of 3.1b

bsearch2.0ms

end0.0ms

sample19.8s

Algorithm
intervals
Results
6.2s2535×body2560valid
5.7s1931×body10240exit
5.5s3489×body1280valid
1.0s1074×body640valid
541.0ms9933×pre80true
269.0ms360×body320valid
75.0ms416×body80valid
55.0ms128×body160valid