Details

Time bar (total: 58.4s)

sample448.0ms

Algorithm
intervals
Results
166.0ms121×body1280valid
156.0ms74×body2560valid
64.0ms43×body10240exit
21.0ms33×body640valid
12.0ms299×pre80true
4.0ms8×body320valid
2.0ms14×body80valid
2.0ms6×body160valid

simplify236.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
235.0ms
(/ (* 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: 35.9b

localize38.0ms

Local error

Found 4 expressions with local error:

30.2b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
19.7b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.0b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* eps a))

rewrite44.0ms

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
21.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
16.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
5.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* eps a))

series891.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
588.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
157.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
110.0ms
(* (expm1 (* (+ a b) eps)) eps)
37.0ms
(expm1 (* eps a))

simplify8.9s

Counts
94 → 120
Calls
94 calls:
Slowest
637.0ms
(/ (/ (* (* (* (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))))
584.0ms
(/ (/ (* (* (* (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))))
404.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
371.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
335.0ms
(- (log (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))) (log (expm1 (* eps b))))

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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
14.0ms
(+ (/ 1 a) (/ 1 b))

series12.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
12.0ms
(+ (/ 1 a) (/ 1 b))

simplify414.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
59.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
29.0ms
(/ (sqrt 1) (* (cbrt a) (cbrt a)))
25.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
24.0ms
(+ (/ (cbrt 1) a) (/ (cbrt 1) b))
19.0ms
(+ (/ (sqrt 1) a) (/ (sqrt 1) b))

prune306.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

18.9b
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
8.1b
(/ (* eps b) a)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
15×times-frac
13×add-sqr-sqrt add-cube-cbrt
9×add-cbrt-cube add-exp-log
6×associate-/r*
5×associate-/l*
4×distribute-lft-out
3×cbrt-undiv div-exp
2×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
1×flip3-+ prod-exp cbrt-unprod flip-+
Counts
2 → 60
Calls
2 calls:
Slowest
42.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
14.0ms
(/ (* eps b) a)

series132.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
97.0ms
(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
35.0ms
(/ (* eps b) a)

simplify3.5s

Counts
51 → 66
Calls
51 calls:
Slowest
477.0ms
(+ (pow (/ (* eps b) a) 3) (pow eps 3))
358.0ms
(- (* (/ (* eps b) a) (/ (* eps b) a)) (* eps eps))
313.0ms
(- (+ (/ 1 b) (/ 1 a)) (* 1/2 (/ (* eps b) a)))
263.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))
249.0ms
(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))

prune660.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

18.8b
(/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps))
8.1b
(/ (* eps b) a)
0.0b
(/ 1 (/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
97×*-un-lft-identity
65×add-sqr-sqrt add-cube-cbrt
25×associate-/r*
21×add-exp-log
16×distribute-lft-out
15×add-cbrt-cube
11×associate-/r/
10×div-exp
7×div-inv associate-/l*
6×cbrt-undiv
5×flip3-+ flip-+
4×pow1
3×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp 1-exp
1×div-sub prod-exp cbrt-unprod pow-flip inv-pow expm1-udef
Counts
3 → 160
Calls
3 calls:
Slowest
48.0ms
(/ 1 (/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps)))
32.0ms
(/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps))
17.0ms
(/ (* eps b) a)

series276.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
142.0ms
(/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps))
108.0ms
(/ 1 (/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps)))
27.0ms
(/ (* eps b) a)

simplify18.5s

Counts
192 → 169
Calls
192 calls:
Slowest
704.0ms
(/ 1 (/ (expm1 (* eps b)) (+ (pow (/ (* eps b) a) 3) (pow eps 3))))
454.0ms
(/ (cbrt 1) (/ (sqrt (expm1 (* eps b))) (cbrt (+ (/ (* eps b) a) eps))))
357.0ms
(/ (* (* 1 1) 1) (* (* (/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps)) (/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps))) (/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps))))
322.0ms
(/ (cbrt 1) (/ (expm1 (* eps b)) (+ (/ (* eps b) a) eps)))
314.0ms
(/ (sqrt 1) (/ (expm1 (* eps b)) (- (* (/ (* eps b) a) (/ (* eps b) a)) (* eps eps))))

prune1.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes178.0ms

Accuracy

-5.4% (3.7b remaining)

Error of 3.7b against oracle of 0.0b and baseline of 3.5b

bsearch504.0ms

end0.0ms

sample19.7s

Algorithm
intervals
Results
6.4s2591×body2560valid
5.8s3420×body1280valid
4.6s1881×body10240exit
1.4s1040×body640valid
579.0ms9882×pre80true
196.0ms344×body320valid
177.0ms479×body80valid
47.0ms127×body160valid