Details

Time bar (total: 1.4m)

sample529.0ms

Algorithm
intervals
Results
170.0ms74×body10240exit
149.0ms86×body2560valid
138.0ms112×body1280valid
30.0ms38×body640valid
14.0ms330×pre80true
3.0ms6×body320valid
2.0ms11×body80valid
1.0ms3×body160valid

simplify259.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
259.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.0b

localize39.0ms

Local error

Found 4 expressions with local error:

27.2b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
16.7b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(* (+ a b) eps)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
30×add-sqr-sqrt
28×*-un-lft-identity
26×add-cube-cbrt
22×add-cbrt-cube add-exp-log
8×pow1 associate-/l*
7×cbrt-undiv div-exp associate-*l*
6×associate-/r* associate-*r* div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative unswap-sqr
1×flip3-+ flip-+ distribute-lft-out associate-/l/
Counts
4 → 120
Calls
4 calls:
Slowest
21.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
18.0ms
(* (+ a b) eps)
12.0ms
(* (expm1 (* (+ a b) eps)) eps)
10.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))

series957.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
652.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
141.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
136.0ms
(* (expm1 (* (+ a b) eps)) eps)
27.0ms
(* (+ a b) eps)

simplify15.0s

Counts
158 → 132
Calls
158 calls:
Slowest
741.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
519.0ms
(/ (/ (* (* (* (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))))
465.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
460.0ms
(/ (/ (* (* (* (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))))
419.0ms
(* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps))

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite19.0ms

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
18.0ms
(+ (/ 1 a) (/ 1 b))

series21.0ms

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

simplify2.0s

Counts
27 → 38
Calls
27 calls:
Slowest
509.0ms
(- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))
412.0ms
(+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))
402.0ms
(* (* (+ (/ 1 a) (/ 1 b)) (+ (/ 1 a) (/ 1 b))) (+ (/ 1 a) (/ 1 b)))
332.0ms
(+ (pow (/ 1 a) 3) (pow (/ 1 b) 3))
31.0ms
(- (/ 1 a) (/ 1 b))

prune284.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

16.7b
(/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
16.2b
(/ eps (expm1 (* eps a)))
6.4b
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
0.0b
(* (+ b a) eps)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
26×*-un-lft-identity
24×add-cube-cbrt
22×times-frac add-cbrt-cube add-exp-log
16×associate-*r*
8×pow1
7×associate-*l*
6×cbrt-undiv associate-/r* div-exp
5×prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×div-inv unswap-sqr
2×clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
1×flip3-+ flip-+ distribute-lft-out associate-/l/
Counts
4 → 116
Calls
4 calls:
Slowest
16.0ms
(/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
16.0ms
(* (+ b a) eps)
11.0ms
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
8.0ms
(/ eps (expm1 (* eps a)))

series900.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
629.0ms
(/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
162.0ms
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
69.0ms
(/ eps (expm1 (* eps a)))
40.0ms
(* (+ b a) eps)

simplify13.5s

Counts
143 → 128
Calls
143 calls:
Slowest
1.2s
(* (* (/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b))) (/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))) (/ (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b))))
479.0ms
(/ (* (* eps eps) eps) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))))
479.0ms
(/ (* (* (* (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))))
442.0ms
(/ (* (* (* (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))))
435.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

17.2b
(* (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (/ 1 (expm1 (* eps b))))
16.2b
(/ eps (expm1 (* eps a)))
6.4b
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
0.2b
(/ 1 (expm1 (* eps b)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log
40×add-sqr-sqrt
37×times-frac
35×*-un-lft-identity add-cube-cbrt
34×add-cbrt-cube
26×associate-*r*
22×prod-exp
14×div-exp
12×pow1 cbrt-unprod
8×cbrt-undiv
6×associate-/r* associate-/l*
4×expm1-log1p-u rec-exp 1-exp associate-*l* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg *-commutative unswap-sqr
1×frac-times associate-*l/ un-div-inv pow-flip inv-pow
Counts
4 → 148
Calls
4 calls:
Slowest
52.0ms
(* (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (/ 1 (expm1 (* eps b))))
10.0ms
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
5.0ms
(/ 1 (expm1 (* eps b)))
4.0ms
(/ eps (expm1 (* eps a)))

series916.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
639.0ms
(* (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (/ 1 (expm1 (* eps b))))
168.0ms
(* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))
59.0ms
(/ eps (expm1 (* eps a)))
49.0ms
(/ 1 (expm1 (* eps b)))

simplify22.8s

Counts
179 → 160
Calls
179 calls:
Slowest
825.0ms
(* (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a)))) (/ 1 (sqrt (expm1 (* eps b)))))
528.0ms
(* (* (* (* (expm1 (* (+ b a) eps)) (expm1 (* (+ b a) eps))) (expm1 (* (+ b a) eps))) (/ (* (* eps eps) eps) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))))) (/ (* (* 1 1) 1) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b)))))
483.0ms
(+ (+ (log (expm1 (* (+ b a) eps))) (- (log eps) (log (expm1 (* eps a))))) (- 0 (log (expm1 (* eps b)))))
473.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
471.0ms
(+ (log (* (expm1 (* (+ b a) eps)) (/ eps (expm1 (* eps a))))) (log (/ 1 (expm1 (* eps b)))))

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (3.5b remaining)

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

bsearch1.0ms

end0.0ms

sample19.7s

Algorithm
intervals
Results
6.2s2573×body2560valid
5.5s1991×body10240exit
5.5s3444×body1280valid
980.0ms1020×body640valid
711.0ms9995×pre80true
200.0ms347×body320valid
87.0ms475×body80valid
54.0ms145×body160valid