Details

Time bar (total: 1.0m)

sample612.0ms

Algorithm
intervals
Results
199.0ms79×body2560valid
184.0ms116×body1280valid
151.0ms80×body10240exit
27.0ms32×body640valid
17.0ms336×pre80true
6.0ms10×body320valid
3.0ms15×body80valid
1.0ms4×body160valid

simplify223.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
223.0ms
(/ (* 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: 36.4b

localize52.0ms

Local error

Found 4 expressions with local error:

31.2b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
19.1b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite30.0ms

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
11.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
9.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
6.0ms
(* (expm1 (* (+ a b) eps)) eps)
1.0ms
(expm1 (* (+ a b) eps))

series952.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
597.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
159.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
135.0ms
(* (expm1 (* (+ a b) eps)) eps)
61.0ms
(expm1 (* (+ a b) eps))

simplify9.5s

Counts
94 → 120
Calls
94 calls:
Slowest
571.0ms
(/ (/ (* (* (* (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))))
563.0ms
(/ (/ (* (* (* (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))))
434.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
387.0ms
(* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps))
356.0ms
(+ (* a (pow eps 2)) (+ (* 1/2 (* (pow a 2) (pow eps 3))) (* (pow eps 2) b)))

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite25.0ms

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
24.0ms
(+ (/ 1 a) (/ 1 b))

series22.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
21.0ms
(+ (/ 1 a) (/ 1 b))

simplify365.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
65.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
18.0ms
(/ 1 (* (cbrt a) (cbrt a)))
18.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt a))
18.0ms
(+ (/ 1 a) (/ 1 b))
17.0ms
(+ (/ 1 a) (/ 1 b))

prune314.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

19.1b
(/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
18.1b
(/ eps (expm1 (* eps a)))
7.7b
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
0.0b
(expm1 (* (+ b a) eps))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×*-un-lft-identity times-frac add-cube-cbrt
20×add-cbrt-cube add-exp-log
13×associate-*r*
6×pow1 cbrt-undiv associate-/r* div-exp
5×log1p-expm1-u
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×associate-*l* div-inv
2×clear-num frac-2neg associate-*r/ unswap-sqr
1×expm1-log1p pow-prod-down *-commutative expm1-udef associate-/l/
Counts
4 → 104
Calls
4 calls:
Slowest
27.0ms
(/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
18.0ms
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
8.0ms
(/ eps (expm1 (* eps a)))
1.0ms
(expm1 (* (+ b a) eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
664.0ms
(/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
178.0ms
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
82.0ms
(/ eps (expm1 (* eps a)))
81.0ms
(expm1 (* (+ b a) eps))

simplify7.4s

Counts
80 → 116
Calls
80 calls:
Slowest
659.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
467.0ms
(/ (* (* eps eps) eps) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))))
458.0ms
(/ (* (* (* (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))))
396.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
391.0ms
(/ (* (* (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))) (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

36.9b
(cbrt (* (/ (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))) (/ (expm1 (* (+ a b) eps)) (* (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))))))
26.7b
(/ (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))))
19.0b
(/ (expm1 (* eps b)) eps)
19.0b
(/ (expm1 (* eps b)) eps)

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
29×add-cbrt-cube add-exp-log
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×times-frac
10×cbrt-undiv div-exp
7×associate-/r* prod-exp cbrt-unprod associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div clear-num frac-2neg div-inv
2×div-sub associate-*l/ expm1-udef
1×cbrt-prod frac-times pow1/3 associate-*r/ associate-/r/
Counts
4 → 106
Calls
4 calls:
Slowest
128.0ms
(cbrt (* (/ (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))) (/ (expm1 (* (+ a b) eps)) (* (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))))))
28.0ms
(/ (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))))
9.0ms
(/ (expm1 (* eps b)) eps)
8.0ms
(/ (expm1 (* eps b)) eps)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
700.0ms
(cbrt (* (/ (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))) (/ (expm1 (* (+ a b) eps)) (* (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))))))
395.0ms
(/ (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))))
59.0ms
(/ (expm1 (* eps b)) eps)
47.0ms
(/ (expm1 (* eps b)) eps)

simplify13.0s

Counts
82 → 118
Calls
82 calls:
Slowest
1.0s
(/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps)))) (* (/ (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))) (* (* eps eps) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))))
951.0ms
(/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps)))) (* (* (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))))
936.0ms
(/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps)))) (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps)))) (* (/ (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))) (* (* eps eps) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))))
839.0ms
(/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps)))) (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps)))) (* (* (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))) (* (/ (expm1 (* eps b)) eps) (expm1 (* eps a)))))
721.0ms
(/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps)))) (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps)))) (* (* (* (/ (expm1 (* eps b)) eps) (/ (expm1 (* eps b)) eps)) (/ (expm1 (* eps b)) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))))

prune1.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

0% (3.4b remaining)

Error of 3.4b against oracle of 0.0b and baseline of 3.4b

bsearch2.0ms

end0.0ms

sample20.2s

Algorithm
intervals
Results
7.0s2525×body2560valid
5.7s2080×body10240exit
5.1s3496×body1280valid
964.0ms1037×body640valid
654.0ms10082×pre80true
303.0ms354×body320valid
110.0ms458×body80valid
50.0ms132×body160valid