Details

sample660.0ms

Algorithm

intervals

Results

212.0ms	72×	body	2560	valid
188.0ms	116×	body	1280	valid
163.0ms	62×	body	10240	exit
40.0ms	42×	body	640	valid
18.0ms	318×	pre	80	true
7.0ms	10×	body	320	valid
3.0ms	12×	body	80	valid
2.0ms	4×	body	160	valid

simplify231.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

231.0ms

(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.9b

localize56.0ms

Local error

Found 4 expressions with local error:

26.2b	(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
15.6b	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b	(* (expm1 (* (+ a b) eps)) eps)
0.0b	(expm1 (* eps a))

rewrite62.0ms

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

28.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
19.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
12.0ms	(* (expm1 (* (+ a b) eps)) eps)
1.0ms	(expm1 (* eps a))

series897.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

596.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
131.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
118.0ms	(* (expm1 (* (+ a b) eps)) eps)
51.0ms	(expm1 (* eps a))

simplify8.9s

Counts

94 → 120

Calls

94 calls:

Slowest

606.0ms	(/ (/ (* (* (* (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))))
591.0ms	(/ (/ (* (* (* (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))))
410.0ms	(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
344.0ms	(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
342.0ms	(* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps))

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

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

26.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

20.0ms

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

simplify425.0ms

Counts

27 → 38

Calls

27 calls:

Slowest

61.0ms	(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
24.0ms	(* (exp (/ 1 a)) (exp (/ 1 b)))
21.0ms	(+ (/ (sqrt 1) a) (/ (sqrt 1) b))
19.0ms	(+ (/ 1 b) (/ 1 a))
19.0ms	(/ (* (cbrt 1) (cbrt 1)) (sqrt a))

prune360.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b	(cbrt (+ (/ 1 a) (/ 1 b)))
0.5b	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `associate-r/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 171

Calls

4 calls:

Slowest

87.0ms	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
13.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
13.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
13.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
117.0ms	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
117.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
109.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))

simplify12.1s

Counts

187 → 183

Calls

187 calls:

Slowest

479.0ms	(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
451.0ms	(* (cbrt (+ (* 1 b) (* a 1))) (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
436.0ms	(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (+ (/ 1 a) (/ 1 b))))
430.0ms	(cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))
424.0ms	(* (cbrt (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))) (cbrt (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

14.9b	(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
5.1b	(/ (* eps b) a)

rewrite44.0ms

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

34.0ms	(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
9.0ms	(/ (* eps b) a)

series149.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

110.0ms	(/ (+ (/ (* eps b) a) eps) (expm1 (* eps b)))
39.0ms	(/ (* eps b) a)

simplify3.6s

Counts

51 → 66

Calls

51 calls:

Slowest

450.0ms	(+ (pow (/ (* eps b) a) 3) (pow eps 3))
355.0ms	(- (* (/ (* eps b) a) (/ (* eps b) a)) (* eps eps))
333.0ms	(- (+ (/ 1 b) (/ 1 a)) (* 1/2 (/ (* eps b) a)))
307.0ms	(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))
293.0ms	(+ (/ eps (- (exp (* eps b)) 1)) (/ (* eps b) (* a (- (exp (* eps b)) 1))))

prune616.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes485.0ms

Accuracy

0% (3.3b remaining)

Error of 3.3b against oracle of 0.0b and baseline of 3.3b

bsearch1.0ms

end0.0ms

sample20.0s

Algorithm

intervals

Results

6.5s	2607×	body	2560	valid
5.7s	3419×	body	1280	valid
5.5s	1989×	body	10240	exit
1.0s	1051×	body	640	valid
511.0ms	9990×	pre	80	true
242.0ms	341×	body	320	valid
116.0ms	135×	body	160	valid
107.0ms	448×	body	80	valid