Details

Time bar (total: 2.0m)

sample591.0ms

Algorithm
intervals
Results
196.0ms81×body2560valid
182.0ms72×body10240exit
140.0ms114×body1280valid
22.0ms27×body640valid
17.0ms328×pre80true
8.0ms13×body320valid
3.0ms18×body80valid
1.0ms3×body160valid

simplify210.0ms

Calls
1 calls:
Slowest
210.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

localize417.0ms

Local error

Found 4 expressions with local error:

27.9b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
17.5b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.1b
(expm1 (* (+ a b) eps))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
300×times-frac
200×add-sqr-sqrt
164×*-un-lft-identity add-cube-cbrt
64×associate-/l*
54×associate-*r* associate-*l*
20×add-cbrt-cube add-exp-log
18×*-commutative unswap-sqr associate-/l/
9×associate-/r*
7×cbrt-undiv div-exp
6×pow1 div-inv
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×clear-num frac-2neg prod-exp cbrt-unprod
1×expm1-log1p pow-prod-down expm1-udef
Calls
4 calls:
Slowest
35.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
26.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
11.0ms
(* (expm1 (* (+ a b) eps)) eps)
1.0ms
(expm1 (* (+ a b) eps))

series983.0ms

Calls
4 calls:
Slowest
618.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
189.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
123.0ms
(* (expm1 (* (+ a b) eps)) eps)
53.0ms
(expm1 (* (+ a b) eps))

simplify35.5s

Calls
412 calls:
Slowest
594.0ms
(/ (/ (* (* (* (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))))
527.0ms
(/ (/ (* (* (* (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))))
471.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) (* (cbrt eps) (cbrt eps))) (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a))))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))
433.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
419.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))

prune4.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-add
56×*-un-lft-identity
54×associate-/r* associate-/l*
46×add-sqr-sqrt add-cube-cbrt
18×clear-num frac-2neg
15×times-frac
13×fma-def
7×distribute-lft-out
5×div-inv
3×add-log-exp
1×expm1-log1p-u pow1 +-commutative sum-log flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u
Calls
1 calls:
Slowest
25.0ms
(+ (/ 1 a) (/ 1 b))

series20.0ms

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

simplify7.7s

Calls
187 calls:
Slowest
795.0ms
(+ (* (/ 1 (* (cbrt a) (cbrt a))) (- b)) (* (cbrt a) (- 1)))
386.0ms
(+ (* (- 1) (cbrt b)) (* (- a) (/ 1 (* (cbrt b) (cbrt b)))))
290.0ms
(+ (* (/ 1 (* (cbrt a) (cbrt a))) (cbrt b)) (* (cbrt a) (/ 1 (* (cbrt b) (cbrt b)))))
257.0ms
(+ (* (/ 1 (* (cbrt a) (cbrt a))) (/ b 1)) (* (cbrt a) 1))
233.0ms
(+ (* (/ 1 (sqrt a)) (- b)) (* (sqrt a) (- 1)))

prune996.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

26.2b
(/ eps (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))))
12.1b
(/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))
0.8b
(* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps))))
0.1b
(expm1 (* (+ a b) eps))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
109×add-sqr-sqrt
86×*-un-lft-identity
84×add-cube-cbrt
65×associate-*r*
32×associate-/r*
20×add-cbrt-cube add-exp-log
18×associate-*r/
15×associate-*l*
14×associate-/l*
11×associate-/r/
10×unswap-sqr
7×div-inv
6×pow1 cbrt-undiv clear-num div-exp
5×*-commutative log1p-expm1-u
4×expm1-log1p-u frac-2neg prod-exp un-div-inv cbrt-unprod insert-posit16 add-log-exp
2×expm1-udef
1×expm1-log1p div-sub pow-prod-down
Calls
4 calls:
Slowest
31.0ms
(/ eps (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))))
20.0ms
(* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps))))
8.0ms
(/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))
0.0ms
(expm1 (* (+ a b) eps))

series581.0ms

Calls
4 calls:
Slowest
216.0ms
(/ eps (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))))
198.0ms
(* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps))))
120.0ms
(/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))
47.0ms
(expm1 (* (+ a b) eps))

simplify20.2s

Calls
254 calls:
Slowest
510.0ms
(/ (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))) (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))))
482.0ms
(/ (* (* eps eps) eps) (* (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))) (/ (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))) (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))))))
478.0ms
(/ (* (cbrt eps) (cbrt eps)) (* (expm1 (* eps b)) (/ (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a)))) (* (cbrt (expm1 (* (+ a b) eps))) (cbrt (expm1 (* (+ a b) eps)))))))
418.0ms
(/ (* (cbrt eps) (cbrt eps)) (* (expm1 (* eps b)) (/ 1 (* (cbrt (expm1 (* (+ a b) eps))) (cbrt (expm1 (* (+ a b) eps)))))))
410.0ms
(/ (* (cbrt eps) (cbrt eps)) (* (expm1 (* eps b)) (/ (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a)))) 1)))

prune2.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

26.1b
(/ (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))) eps)
12.1b
(/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))
0.8b
(* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps))))
0.1b
(expm1 (* (+ a b) eps))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
109×add-sqr-sqrt
86×*-un-lft-identity
84×add-cube-cbrt
65×associate-*r*
34×associate-/l*
20×add-cbrt-cube add-exp-log
18×associate-*r/
15×associate-*l*
12×associate-/r*
11×associate-/l/
10×unswap-sqr
7×div-inv
6×pow1 cbrt-undiv clear-num div-exp
5×*-commutative log1p-expm1-u
4×expm1-log1p-u frac-2neg prod-exp un-div-inv cbrt-unprod insert-posit16 add-log-exp
2×expm1-udef
1×expm1-log1p div-sub pow-prod-down
Calls
4 calls:
Slowest
26.0ms
(/ (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))) eps)
11.0ms
(* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps))))
5.0ms
(/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))
0.0ms
(expm1 (* (+ a b) eps))

series611.0ms

Calls
4 calls:
Slowest
214.0ms
(/ (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))) eps)
198.0ms
(* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps))))
124.0ms
(/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))
74.0ms
(expm1 (* (+ a b) eps))

simplify22.3s

Calls
252 calls:
Slowest
583.0ms
(/ (* (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))) (/ (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))) (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))))) (* (* eps eps) eps))
508.0ms
(/ (* (expm1 (* eps b)) (/ 1 (* (cbrt (expm1 (* (+ a b) eps))) (cbrt (expm1 (* (+ a b) eps)))))) (* (cbrt eps) (cbrt eps)))
476.0ms
(/ (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))) (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))))
474.0ms
(/ (* (expm1 (* eps b)) (/ (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a)))) (* (cbrt (expm1 (* (+ a b) eps))) (cbrt (expm1 (* (+ a b) eps)))))) (* (cbrt eps) (cbrt eps)))
456.0ms
(/ (* (* (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps)))) (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps))))) (* (expm1 (* eps b)) (/ (expm1 (* eps a)) (expm1 (* (+ a b) eps))))) (* (* eps eps) eps))

prune3.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes128.0ms

Accuracy

-32.6% (4.8b remaining)

Error of 4.8b against oracle of 0.0b and baseline of 3.6b

bsearch369.0ms

end0.0ms

sample19.6s

Algorithm
intervals
Results
6.6s2590×body2560valid
5.8s1976×body10240exit
4.8s3334×body1280valid
1.1s1090×body640valid
614.0ms9981×pre80true
221.0ms379×body320valid
87.0ms485×body80valid
52.0ms127×body160valid